Physics SSC I -

Physics Notes Class 9

Unit 1

Q What is science?

The word science derived from the Latin word “Scientia” which means knowledge. The knowledge gained through observations and experimentation is called science.

Q What do you know about the natural philosophy?

Initially, the observations of man about the world around him give birth to the single discipline of science, called natural philosophy.

Q Define the two main streams of natural philosophy.

Science is divided into two main streams:

• Biological Sciences

• Physical Sciences

Biological Sciences:

The branch of science which concerns with the study of living things is called biological sciences.

Physical Sciences:

The branch of science which deals with the study of non-living things is called physical sciences.

Q Define Physics, and write a detail note on branches of Physics.

Physics is that branch of science, which deals with the study of properties of matter, energy and their mutual relationship.

BRANCHES OF PHYSICS:

Mechanics:

It is the study of motion of objects, its causes and effects.

Heat:

It deals with the nature of heat, modes of transfer and effects of heat.

Sound:

It deals with the physical aspects of sound waves, their production, properties and applications.

Light (Optics):

It is the study of physical aspects of light, its properties, working and use of optical instruments.

Electricity and Magnetism:

It is the study of the charges at rest and in motion, their effects and their relationship with magnetism.

Atomic Physics:

It is the study of the structure and properties of atoms.

Nuclear Physics:

It deals with the properties and behaviour of nuclei and the particles within the nuclei.

Plasma Physics:

It is the study of production, properties of the ionic state of matter – the fourth state of matter.

Geophysics:

It is the study of the internal structure of the Earth.

Q Describe the role of Physics in the progress of science.

Physics played pivotal role in the progress of science. The rapid progress in science during the recent yeas has become possible due to the discoveries and inventions in the field of Physics. The technologies are the applications of scientific principles. Most of the technologies of our modern society throughout the world are related to Physics.

Q Describe the role of Physics in making our lives easier, faster and more comfortable than past.

Physics make our lives easier, faster and more comfortable than past.

Pulleys make it easy to lift heavy loads.
Means of transportation were constructed on the basic principle of Physics.
Mobile phones enable us to contact people anywhere in the world and get latest worldwide information.

Q Which scientific inventions have caused harms and destruction of serious nature to human’s society?

The scientific inventions that caused harms and destruction of serious nature are:

Environmental Pollution
Weapons of Mass Destruction

Q Why do we study physics?

The rapid progress in science during the recent years has become possible due to the discoveries and inventions in the field of Physics. The technologies are the applications of scientific principles. Most of the technologies of our modern society throughout the world are related to Physics. For example, a car is made on the principles of mechanics and a refrigerator is based on the principles of thermodynamics.

Q Name any five branches of physics.

Branches of Physics:

Mechanics
Heat
Sound
Atomic Physics
Plasma Physics

Q What do you know about physical quantities?

All measureable quantities are called physical quantities such as length, mass, time and temperature. Physical quantities are divided into base and derived quantities.

Q Describe the characteristics that are common in all physical quantities.

A physical quantity possesses at least characteristics in common. One is its numerical value and the other is the unit in which it is measured. For example, if the length of the student is 104 cm then 104 is its numerical magnitude and centimeter is the unit of measurement.

Q Define the term Unit.

Once a standard is set for a quantity then it can be expressed in terms of that standard quantity. This standard quantity is called a unit.

Q What do you know about International system of Units (SI)?

In 1960, the General Conference on Weight and Measure adopted a world-wide system of measurements is known as international system of units (SI).

Q Write a note on Base Units.

Base Units:

The units that describe base quantities are called as base units. Base units are seven in numbers. The base units corresponding to base quantities are given in the table.

Quantity		Unit
Name	symbol	Name	symbol
Length	l	Meter	m
Mass	m	Kilogram	kg
Time	t	Seconds	s
Electric Current	I	Ampère	A
Intensity of light	L	Candela	cd
Temperature	T	Kelvin	K
Amount of Substance	n	Mole	mol

Q Write a note on Derived Units.

Derived Units:

The units used to measure derived quantities are called derived units. Derived units are numerous. The derived units corresponding to derived quantities are given in the table:

Quantity		Unit
Name	symbol	Name	symbol
Speed	V	Meter per second	ms^-1
Volume	V	Cubic meter	m³
Acceleration	A	Meter per second per second	ms^-2
Force	F	Newton	N or ( Kg ms^-2)
Pressure	P	Pascal	Pa or ( Nm^-2)
Density	Ρ	Kilogram per cubic meter	Kgm^-3
Charge	Q	Coulomb	C or ( As)

Q How can you differentiate between base and derived quantities?

Base Quantities	Derived Quantities
The base quantities are those physical quantities in terms of which other physical quantities are defined.	The quantities that are derived from the base quantities are called derived quantities.
Examples: Mass, length, time	Examples: Velocity, acceleration, force

Q Identify the base quantity in the following:

(i) Speed (ii) Area (iii) Force (iv) Distance

Base quantities isDistance.

Q Identify the following as base or derived quantity:

Density, force, mass, speed, time, length, temperature and volume.

Basequantity	Mass, length, time and temperature.
Derivedquantity	Density, force, speed and volume

Q What are prefixes? Give examples.

The word or letters added before a unit and stands for the multiples or sub-multiples of that unit are known as prefixes. The prefixes are useful to express very large or small quantities.

Prefix	Symbol	Multiplier
exa	E	10¹⁸
peta	P	10¹⁵
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
hecto	h	10²
deca	da	10¹
deci	d	10^-1
centi	c	10^-2
milli	m	10^-3
micro		10^-6
nano	n	10^-9
pico	p	10^-12
femto	f	10^-15
atto	a	10^-18

Example:

Q What do you know about scientific natation? Give it with examples.

In scientific notation, a number is expressed as some power of ten multiplied by a number between 1 and 10.

Example:

The scientific notation of the measurement 384000000 m is 3.84 x 10⁸m.
The scientific notation of the measurement 0.00045 is 4.5 x 10^-4s.

Significance: Scientific notation saves writing down or interpreting large number of zeros.

Q Name five prefixes most commonly used.

Prefixes most commonly used are:

giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10^-2
milli	m	10^-3

Q The Sun is one hundred and fifty million kilometres away from the Earth. Write this

(a) as an ordinary whole number.

(b) in scientific notation.

In ordinary whole number: 150,000,000km = 150,000,000,000m

In scientific notation:

Q Write the numbers given below in scientific notation.

(a) 3000000000 ms^-1 (b) 6400000 m

(c) 0.0000000016 g (d) 0.0000548 s

(a)

(b)

(c)

(d)

Q What are measuring instruments?

Measuring instruments are used to measure various physical quantities such as length, mass, time, volume etc. The measuring instruments used in Physics laboratory are meter rule, measuring tape, verniercalliper, screw gauge, physical balance, lever balance, electronic balance, stop watch and measuring cylinder etc.

Q What is metre rule?

A meter rule is a length measuring instrument. It is commonly used in the laboratories to measure length of an object or distance between two points. It is one metre long which is equal to100 centimetres. Each centimetre (cm) is divided into 10 small divisions called millimetre (mm).

Q What is least count of metre rule?

Metre rule is one metre long which is equal to100 centimetres. Each centimetre (cm) is divided into 10 small divisions called millimetre (mm).

Q Which precautions should be carried out while measuring length with meter rule?

When measuring length, or distance, eye must be kept vertically above the reading point. The reading becomes doubtful if the eye is positioned either left or right to the reading point.

Q What is measuring tape?

Measuring tapes are used to measure length in meters and centimetres. A measuring tape consists of a thin and long strip of cotton, metal or plastic generally 10 m,20 m, 50 m, or 100 m long.

Q What is a vernier calliper?

Vernie rcalliper is a length measuring instrument used to measure the length. A VernierCallipers consists of two jaws. One is a fixed jaw with main scale attached to it. Main scale has centimetre and millimetre marks on it. The other jaw is a moveable jaw. It has vernier scale having 10 divisions over it such that each of its division is 0.9 mm. The difference between one small division on main scale division and one vernier scale division is 0.1 mm. It is called least count (L.C) of the vernier callipers.

Q Define least count of vernier callipers.

The difference between one small division on main scale division and one vernier scale division is 0.1 mm. It is called least count (LC) of the verniercallipers. Least count of vernier calipers can also be found as:

Q What is zero error of vernier callipers?

To find the zero error, close the jaws of vernier callipers gently. Zero error will exist if zero line of the vernier scale is not coinciding with the zero of main scale.

Q What is positive zero error of vernier callipers?

Zero error will be positive if zero line of vernier scale is on the right side of the zero of the main scale.

Q What is negative zero error of vernier callipers?

Zero error will be negative if zero line of vernier scale is on the left side of zero of the main scale.

Q What is the range of the Vernier Callipers used in your Physics laboratory?

Least count of vernier calipers is 0.1mm or 0.01cm.

Q How many divisions are there on its vernier scale?

There are 10 divisons on its vernier scale.

Q Why do we use zero correction?

We use zero correction to take correct and accurate measurements.

Q Which is more precise a digital vernier callipers or a mechanical vernier callipers?

Least count of mechanical vernier calliper is 0.1mm and least count of digital vernier calliper is 0.01mm. Digital Vernier Callipers has greater precision than mechanical Vernier Callipers due to smaller least count.

Q What is screw gauge?

The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or the thickness of a sheet of metal. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble. Parallel to the axis of the thimble, a scale graduated in mm is engraved.

Q What are the uses of screw gauge?

Screw gauge is used to measure:

Diameter
Thickness
Length

Q Define pitch of screw gauge.

The distance between consecutive threads on the spindle is 1 mm. This distance is called the pitch of screw on the spindle.

Q What is zero error of screw gauge?

Close the gap between the spindle and the stud of the screw gauge by rotating the ratchet in the clockwise direction. If zero of circular scale does not coincide with the index line, then there will be zero error.

Q What is positive zero error of screw gauge?

Zero error will be positive if zero of circular scale is behind the index line. In this case, multiply the number of divisions of the circular scale that has not crossed the index line with the least count of screw gauge to find zero error.

Q What is negative zero error of screw gauge?

Zero error will be negative if zero of circular scale has crossed the index line. In this case, multiply the number of divisions of the circular scale that has crossed the index line with the least count of screw gauge to find the negative zero error.

Q Define least count of screw gauge. How it can be calculated?

Least count is the minimum measurement which can be measured accurately with the help of screw gauge. It can be calculated as:

Q What is the pitch of your laboratory screw gauge?

Pitch of laboratory screw gauge is 1mm.

Q What is the range of your laboratory screw gauge?

The range of laboratory screw gauge is up to 0.01mm or 0.001cm

Q Which one of the two instruments is more precise and why?

(a) Vernier calipers

(b) Screw gauge

Least count of vernier calliper is 0.1mm and least count of screw gaugeis 0.01mm. Screw gaugeis more precise due to smaller least count.

Q Which one of the two instruments is more precise and why?

(a) Ruler

(b) Vernier calipers

(c) Micrometer screw gauge

Least count of ruler is 1 mm. It is 0.1 mm for Vernier Callipers and 0.01mm for micrometerscrew gauge. Thus measurements takenby micrometer screw gaugeare the most precise than the other two.

Q What is a physical balance?

A physical balance is used in the laboratory to measure the mass of various objects by comparison. It consist of a beam resting at the centre on a fulcrum. The beam carries scale pans over the hooks on ether side. Unknown mass is placed on the left pan. Find some suitable standard masses that causes the pointer to remain at zero on raising the beam.

Q What is the function of balancing screws in a physical balance?

Function of balancing screws is to balance a physical balance.

Q On what pan we place the object and why?

We place object in the left pan and standard mass in the right pan. So that we can measure the mass of unknown object.

Q Write a note on lever balance.

A lever balance consists of a system of levers. When lever is lifted placing the object in one pan and standard masses on the other pan, the pointer of the lever system moves. The pointer is brought to zero by varying standard masses.

Q Write a note on Electronic Balance.

Electronic balance come in various ranges: milligram ranges, gram ranges and kilogram ranges.Before measuring the mass of a body, it is switched ON and its reading is set to zero. Next place the object to be weighed. The reading on the balance gives us the mass of the body placed over it.

Q Which balance is more precise explain answer with the help of example?

(a) Beam Balance

(b) Physical Balance

(c) Electronic Balance

The mass of one rupee coin is done using different balances as given below:

(a) Beam Balance:

Let the balance measures coin’s mass = 3.2 g

A sensitive beam balance may be able to detect a change as small as of 0.1 g or

100 mg.

(b) Physical Balance:

Let the balance measures coin’s mass = 3.24 g

Least count of the physical balance may be as small as 0.01 g or 10 mg. Therefore, its measurement would be more precise than a sensitive beam balance.

Let the balance measures coin’s mass = 3.247 g

Least count of an electronic balance is 0.001 g or 1 mg. Therefore, its measurement would be more precise than a sensitive physical balance. Thus, electronic balance is the most sensitive balance in the above balances.

Q Differentiate between physical balance and electronic balance.

Sr. #	Physical Balance	Electronic Balance
1.	Physical balance is a modified type of beam balance used to measure small masses by comparison with greater accuracy.	An electronic machine, which gives us direct reading of mass as we place the objects over it is called electronic balance.
2.	It is less sensitive.	It is more sensitive.
3.	Least count of physical balance is 0.01 or 10mg.	Leas count of electronic balance is 0.001g or 1mg.
4.	A laboratory balance is an example of physical balance.	The balances used in sweet and grocery shops are example of electronic balances.

Q What is stopwatch?

A stopwatch is used to measure the time interval of an event. There are two types of stopwatches:

A mechanical stopwatch can measure a time interval up to a minimum 0.1 second.
Digital stopwatches commonly used in laboratory can measure a time interval as small as 1/100 second or 0.01 second.

Q How to use a mechanical stopwatch?

A mechanical stopwatch has a knob that is used to wind the spring that powers the watch. It can also be used as a start-stop and reset button. The watch starts when the knob is pressed once. When pressed second time, it stops the watch while the third press brings the needle back to zero position.

Q How to use a digital stopwatch?

The digital stopwatch starts to indicate the time lapsed as the start/stop button is pressed. As soon as start/stop button is pressed again, it stops and indicates the time interval recorded by it between start and stop of an event. A reset button restores its initial zero setting.

Q What is measuring cylinder?

A measuring cylinder is a glass or transparent plastic cylinder. It has a scale along its length that indicates the volume in milliliter (ml).

Q What is the use of measuring cylinder?

It is used to measure the volume of a liquid or powdered substance. It is also used to find the volume of an irregular shaped solid insoluble in a liquid by displacement method.

Q What are the precautionary measures should be taken while measuring the volume by using measuring cylinder?

While using a measuring cylinder, it must by kept vertical on a plane surface. The correct method to note the level of a liquid in the cylinder is to keep the eye at the same level as the meniscus of the liquid.It is incorrect to note the liquid level keeping the eye above the level of liquid. When the eye is above the liquid level, the meniscus appears higher on the scale. Similarly, when the eye is below the liquid level, the meniscus appears lower than actual height of the liquid.

Q Can we use the measuring cylinder to determine the volume of an irregular shaped solid?

Ans. Measuring cylinder can be used to find the volume of a small irregular shaped solid that sinks in water. Initially the volumeof water in cylinder is noted. A small solid (stone) tie with thread is lowered into the cylinder till it is fully immersed in water and new reading of volumeis measured. After that the volumeof irregular shaped object is calculated using expression.

Q On what factors accuracy in measuring a physical quantity depends

The accuracy in measuring a physical quantity depends upon various factors:

the quality of the measuring instrument
the skill of the observer
the number of observations made

Q How is precision related to significant figures in a measured quantity?

The greater the number of significant figures, the greater the precision. Each significant figure increases the precision by a factor of ten.

Q Write down the rules for identifying significant figure.

The following rules are helpful in identifying significant figure:

(i) Non-zero digits are always significant.

(ii) Zeros between two significant figures are also significant.

(iii) Final or ending zeros on the right in decimal fraction are significant.

(iv) Zeros written on the left side of the decimal point for the purpose of spacing the decimal point are not significant.

(v) In whole numbers that end in one or more zeros without a decimal point. These zeros may or may not be significant. In such cases, it is not clear which zeros serve to locate the position value and which are actually parts of the measurement. In such a case, express the quantity using scientific notation to find the significant zero.

Q Name any four safety equipment’s that a school laboratory must have?

The safety equipment that a school laboratory must have are:

First aid box
Fire alarm
Fire extinguisher
Sand and water buckets
Waste-disposal basket

Q Write down the laboratory safety rules.

Following are the laboratory safety rules.

Do not carry out any experiment without the permission of your teacher.
Do not eat, drink, play or run in the laboratory.
Read the instructions carefully to familiarize yourself with the possible hazards before handling equipments and materials.
Handle equipments and materials with care.
Do not hesitate to consult your teacher in case of any doubt.
Do not temper with the electrical appliances and other fittings in the laboratory.
Report any accident or injuries immediately to your teacher.

Q Write down the rules for rounding off the numbers.

(i) lf the last digit is less than 5 then it is simply dropped. This decreases the number of significant digits in the figure.

For example:

1.943 is rounded to 1.94

(ii) If the last digit is greater than 5, then the digit on its left is increased by one. This also decreases the number of significant digits in the figure.

For example:

1.47 is rounded to two significant digits 1.5

(iii) If the last digit is 5, then it is rounded to get nearest even number.

For example

1.35 is rounded to 1.4

1.45 is also rounded to 1.4

Exercise

1. Encircle the correct answer from the given choices.

c	b	d	c	d
b	c	c	c	c

1. What is the difference between base quantities and derived quantities? Give three examples in each case.

Base Quantities	Derived Quantities
The base quantities are those physical quantities in terms of which other physical quantities are defined.	The quantities that are derived from the base quantities are called derived quantities.
Examples: Mass, length, time	Examples: Velocity, acceleration, force

1.3 Pick out the base units from the following:

Joule, Newton, kilogramme, hertz, mole, ampere, metre, Kelvin, coulomb and watt.

Base Units:

Kilogram, mole, ampere, metre and Kelvin are the base units.

1.4 Find the base quantities involved in each of the following derived quantities:

(a) speed (b) volume

(c) force (d) work

Derived Quantity	Formula	Base Quantities
Speed		Distance and time
Volume		length
Force		Mass, length and time
Work	F.d	Mass, length and time

1.5 Estimate your age in seconds?

The age of a person in seconds can be find out by expression:

If age of a student of 9th class is 15 years, then:

1.6 What role SI units have played in the development of science?

With the developments in the field of science and technology, the need for a commonly acceptable system of units was seriously felt all over the world particularly to exchange scientific and technical information. SI units made easier to share technical and scientific information all over the world.

1.7 What is meant by Vernier Constant?

The difference between one small division on main scale of verniercalliper and one vernier scale division is 0.1mm and 0.01cm. This is called least count or vernier constant. This is the minimum length which can be measured accurately with the help of vernier caliper.

1.8 What do you understand by the zero error of a measuring instrument?

When zero of moveable scale does not coincide with main scale, then instrument has error. This error is known as zero error of a measuring instrument. For example when jaws of a VernierCallipers or Screw Gauge are closed zero of main scale does not coincide with vernier scale or circular scale then there is zero error in an instrument.

1.9 Why the use of zero error is necessary in measuring instrument?

Mostly measuring instruments have error. To remove this error we use zero correction to take correct measurement.

1.10 What is a stopwatch? What is the least count of a mechanical stopwatch you have used in the laboratories?

A stopwatch is used to measure the time interval of an event.Mechanical stopwatches have least count up to 0.1 seconds.

1.11 Why do we need to measure extremely small intervals of time?

We measure extremely small intervals of time in order to get accurate result and more precise calculations.

1.12 What is meant by Significant Figures of a measurement?

All the accurately known digits and the first doubtful digit in an expression are called significant figures. It reflects the precision of a measured value of a physical quantity.

Example:

0.03 has 1 significant figure
0.274 has 3 significant figures

1.13 How is precision related to the significant in a measured quantity?

An improvement in the quality of measurement by using better instrument increases the significant figures in the measured results. The significant figures are all the digits are known accurately and the one estimated digit. More significant figures mean more precision.

Unit 2

Q Define kinematics.

Kinematics:

Kinematics is the study of motion of an object without discussing the cause of motion.

Q Define rest and motion with examples.

Rest:

A body is said to be at rest, if it does not change its position with respect to its surroundings.

Example:

A book lying on a table.
An electric pole.

Motion:

A body is said to be in motion, if it changes its position with respect to its surroundings.

Example:

A moving car.
The moon revolving around earth.

Q Explain how the state of rest and motion of a body is relative? OR

Give an example of a body that is at rest and in motion at a same time.

A passenger sitting in a moving bus is at rest because he/she is not changing his/her position with respect to other passengers or objects in the bus. But to an observer outside the bus, the passengers and the objects inside the bus are in motion.

Q Describe types of motion with examples.

There are three types of motion.

Translatory motion (linear, random and circular)
Rotatory motion
Vibratory motion (to and fro motion)

Translatory motion:

In translational motion, a body moves along a line without any rotation. The line may be straight or curved.

Example:

Motion of riders in a Ferris wheel.
Motion of a car in a straight line.

Types:

Translatory motions can be divided into linear motion, circular motion and random motion.

Linear motion:

Straight line motion of a body is known as its linear motion.

Example:

Motion of a car on a straight and level road.
Aeroplanes flying straight in air.
Objects falling vertically downward.

Circular motion:

The motion of an object in a circular path is known as Circular motion.

Example:

A stone tied at the end of a string moves in a circle.
A toy train moving on a circular track.
Motion of the Earth around the Sun.

Random motion:

The disordered or irregular motion of an object is called random motion.

Example:

Motion of insects.
Motion of gas molecules.
Motion of birds.

Rotatory Motion:

The spinning motion of a body about its axis is called its rotatory motion.

Example:

Motion of wheel
Motion of steering
Motion of top

Vibratory Motion:

To and fro motion of a body about its mean position is known as vibratory motion.

Example:

Child and a swing
Motion of the pendulum of a clock
Motion of see-saw

Q What is Brownian motion?

According to kinetic molecular model of matter, the molecules remain in continuous motion. Their motion is random. This random motion of gas molecules is called Brownian motion.

Q What is the difference between circular motion and rotatory motion?

Circular Motion	Rotatory Motion
The motion of an object in a circular path is known as Circular motion.	The spinning motion of a body about its axis is called its rotatory motion.
The point about which a body goes around is outside the body.	The line around which a body moves about is passing through the body itself.
For example: A toy train moving on a circular track and Motion of the Earth around the Sun.	For example: Motion of wheel and Motion of top.

Q Mention the type of motion in each of the following.

A ball moving vertically upward.

Linear motion.

A child moving down a slide.

Linear motion.

Movement of a player in a football ground.

Random motion.

The flight of a butterfly.

Random motion.

An athlete running in a circular track.

Circular motion.

The motion of a wheel.

Rotatory motion.

The motion of a cradle.

Vibratory motion.

Q How vectors can be represented?

Symbolic representation:

To differentiate a vector from a scalar quantity, we generally use bold letters to represent vector quantities, such as F, a, d or a bar or arrow over their symbols such as , , , or

Graphical Representation:

Graphically, a vector can be represented by a line segment with an arrow head. As in figure, the line AB with arrow head at B represents a vector V. The length of the line AB gives the magnitude of the vector V on a selected scale. While the direction of the line from A to B gives the direction of the vector V.

Q What is position?

The term position describes the location of a place or a point with respect to some reference point called origin.

Q What is uniform speed?

A body has uniform speed if it covers equal distances in equal intervals of time however short the interval may be.

Q What is uniform velocity?

A body has uniform velocity if it covers equal displacement in equal intervals of time however short the interval may be.

Q What is LIDAR gun?

A LIDAR gun is light detection and ranging speed gun. It uses the time taken by laser pulse to make a series of measurements of a vehicle’s distance from the gun. The data is then used to calculate the vehicle’s speed.

Q When does a body possess acceleration?

In many cases the velocity of a body changes due to a change either in its magnitude or direction or both. The change in the velocity of a body causes acceleration in it.

Q What is acceleration?

Definition:

Acceleration is defined as the rate of change of velocity of a body.

Mathematically:

Unit:

Its SI unit is

Q What is positive acceleration?

Acceleration of a body is positive if its velocity increases with time. The direction of this acceleration is the same in which the body is moving without change in its direction.

Q What is deceleration or retardation?

Acceleration of a body is negative if velocity of the body decreases. The direction of negative acceleration is opposite to the direction in which the body is moving. Negative acceleration is also called deceleration or retardation.

Q What is the direction of acceleration when velocity is increasing and decreasing?

Acceleration of a body is positive if its velocity increases with time. The direction of this acceleration is the same in which the body is moving without change in its direction. Acceleration of a body is negative if velocity of the body decreases. The direction of negative acceleration is opposite to the direction in which the body is moving.

Q What is uniform acceleration?

A body has uniform acceleration if it has equal changes in velocity in equal intervals of time however short the interval may be.

Explanation:

The average acceleration of a body given by equation,

isa during time t. Let the time t is divided into many smaller intervals of time. If the rate of change of velocity during all these intervals remains constant then the acceleration a also remains constant. Such a body is said to possess uniform acceleration.

Q What is graph? Explain types of variables

Graph is a pictorial way of presenting information about the relation between various quantities.

Variable:

The quantities between which a graph is plotted are called the variables.

Independent Variable:

A variable whose value does not depend on that of another is called the independent quantity.

Dependent Variable:

A variable which varies with the independent quantity is called the dependent quantity.

Q What are the uses of graph in our everyday life?

A graph is used in everyday life such as to show year-wise growth/ decline of export, month-wise rainfall, a patient’s temperature record or runs per over scored by a team and so on.

Q Write a note on Distance-Time Graph.

It is useful to represent the motion of objects using graphs. The terms distance and displacement are used interchangeably when the motion is in a straight line. Similarly if the motion is in a straight line then speed and the velocity are also used interchangeably. In a distance-time graph, time is taken along horizontal axis while vertical axis shows the distance covered by the object.

Object At Rest:

The distance moved by the object with time is zero. That is, the object is at rest. Thus, a horizontal line parallel to time axis on a distance-time graph shows that speed of the object is zero.

Object Moving With Constant Speed:

The speed of an object is said to be constant if it covers equal distances in equal intervals of time. The distance-time graph is a straight line. Its slope gives the speed of the object.

Object Moving With Variable Speed:

When an object does not cover equal distances in equal intervals of time then its speed is not constant. In this case the distance-time graph is not a straight line. The slope of the curve at any point can be found from the slope of the tangent at that point.

Q What do you know about Speed-Time graph?

In a speed-time graph, time is taken along x-axis and speed is taken along y-axis.

Object Moving With Constant Speed:

When the speed of an object is constant with time, then the speed-time graph will be a horizontal line parallel to time-axis along x-axis. In other words, a straight line parallel to time axis represents constant speed of the object.

Object Moving With Uniformly Changing Speed (uniform acceleration):

Let the speed of an object be changing uniformly. In such a case speed is changing at constant rate. Thus its speed-time graph would be a straight line. A straight line means that the object is moving with uniform acceleration. Slope of the line gives the magnitude of its acceleration.

Distance Traveled by a Moving Object:

The area under a speed-time graph represents the distance traveled by the object. If the motion is uniform then the area can be calculated using appropriate formula for geometrical shapes represented by the graph.

Q What is gravitational acceleration?

The acceleration of freely falling bodies is called gravitational acceleration. It is denoted by g. On the surface of the Earth, its value is approximately 10 ms^-2. For bodies falling down freely g is positive and is negative for bodies moving up.

Q Write down the equations of motion for bodies moving under gravity.

Equations of motion for bodies moving under gravity are:

Exercise

2.1 Encircle the correct answer from the given choices.

c	b	c	c	b	a
c	c	b	d	a	b

2.2 Explain translatory motion and give examples of various types of translator motion.

Translatory motion:

In translational motion, a body moves along a line without any rotation. The line may be straight or curved.

Example:

Motion of riders in a Ferris wheel.
Motion of a car in a straight line.

Types:

Translatory motions can be divided into linear motion, circular motion and random motion.

Linear motion:

Straight line motion of a body is known as its linear motion.

Example:

Motion of a car on a straight and level road.
Aeroplanes flying straight in air.
Objects falling vertically downward.

Circular motion:

The motion of an object in a circular path is known as Circular motion.

Example:

A stone tied at the end of a string moves in a circle.
A toy train moving on a circular track.
Motion of the Earth around the Sun.

Random motion:

The disordered or irregular motion of an object is called random motion.

Example:

Motion of insects.
Motion of gas molecules.
Motion of birds.

2.3 Differentiate between the following:

(i) Rest and motion.

Rest	Motion
A body is said to be at rest, if it does not change its position with respect to its surroundings.	A body is said to be in motion, if it changes its position with respect to its surroundings.
It is stationary.	It is not stationary.
Example: A book lying on a table and an electric pole.	Example: A moving car and the moon revolving around earth.

(ii) Circular motion and rotatory motion.

Circular Motion	Rotatory Motion
The motion of an object in a circular path is known as Circular motion.	The spinning motion of a body about its axis is called its rotatory motion.
The point about which a body goes around is outside the body.	The line around which a body moves about is passing through the body itself.
For example: A toy train moving on a circular track and Motion of the Earth around the Sun.	For example: Motion of wheel and Motion of top.

(iii) Distance and displacement.

Distance	Displacement
Length of a path between two points is called the distance between those points.	Displacement is the shortest distance between two points which has magnitude and direction.
It is a scalar quantity.	It is a vector quantity.
It is represented by S.	It is represented by d.
It has no direction.	It has direction from initial to final point.
It is the length of path between two points.	It is the shortest distance between two points.

(iv) Speed and velocity.

Speed	Velocity
The distance covered by an object in unit time is called its speed.	The rate of displacement of a body is called its velocity.
It is a scalar quantity.	It is a vector quantity.
It is represented by v.	It is represented by v.
Mathematically:	Mathematically:

Linear Motion	Random Motion
Straight line motion of a body is known as its linear motion.	The disordered or irregular motion of an object is called random motion.
Example: Motion of a car on a straight and level road and objects falling vertically downward.	Example: Motion of insects and motion of gas molecules.

(v) Linear and random motion.

(vi) Scalars and vectors.

Scalar Quantity	Vector Quantity
A scalar quantity is described completely by its magnitude only.	A vector quantity is described completely by magnitude and direction.
It changes with the change in their magnitude.	It changes with the change in their direction or magnitude or both.
For example: mass, length, time, speed, volume, work and energy.	For example: velocity, displacement, force, momentum, torque, etc.

2.4 Define the terms speed, velocity, and acceleration.

Speed:

The distance covered by an object in unit time is called its speed.

It is a scalar quantity.
It is represented by v.

Mathematically:

Unit:

SI unit of speed is

Velocity:

The rate of displacement of a body is called its velocity.

It is a vector quantity.
It is represented by v.

Mathematically:

Unit:

SI unit of velocity is

Acceleration:

Acceleration is defined as the rate of change of velocity of a body.

Mathematically:

Unit:

Its SI unit is

2.5 Can a body moving at a constant speed have acceleration?

Yes, when a body is moving in a circular path with constant speed have acceleration. Its speed remain constant but its direction changes continuously. So a body possesses acceleration.

2.6 How do riders in a Ferris wheel possess translatory motion but not rotatory motion?

In translatory motion, a body moves along a line without any rotation. The line may be straight or curved.Riders in a Ferris wheel possess translatory motion but not rotatory motion because their motion is in a circle without any rotation.

2.7 Sketch a distance-time graph for a body starting from rest. How will you determine the speed of a body from this graph?

The distance-time graph for a body starting from rest:

Speed of the object can be determined by finding the slope.

The speed found from the graph is 2ms^-1

2.8 What would be the shape of a speed – time graph of a body moving with variablespeed?

Object Moving With Variable Speed:

Hence the shape of a speed – time graph of a body moving with variable speed is zigzag.

2.9 Which of the following can be obtained from speed – time graph of a body?

(i) Initial speed.

(ii) Final speed.

(iii) Distance covered in time t.

(iv) Acceleration of motion.

From speed – time graph of a body we can calculate:

(i) Initial speed.

(ii) Final speed.

(iii) Distance covered in time t.

(iv) Acceleration of motion.

2.10 How can vector quantities be represented graphically?

2.11 Why vector quantities cannot be added and subtracted like scalar quantities?

Scalars quantities are added or subtracted only by simple arithmetic methods because scalar quantities have no direction. Since vectors have magnitude as well as direction, therefore vectors cannot be added and subtracted like scalar quantities. Vectors can be added or subtracted by head to tail rule.

2.12 How are vector quantities important to us in our daily life?

Vector quantities are important in our daily life. It would be meaningless to describe vectors without direction. For example, distance of a place from reference point is insufficient to locate that place. The direction of that place from reference point is also necessary to locate it.

2.13 Derive equations of motion for uniformly accelerated rectilinear motion.

Consider a body moving with initial velocity in a straight line with uniform acceleration a. Its velocity becomes v after time t. The motion of body is described by speed-time graph by line AB. The slope of line AB is acceleration a. The total distance covered by the body is shown by the shaded area under the line AB. Equations of motion can be obtained from this graph.

First Equation Of Motion:

Slope of line AB gives the acceleration ‘a’ of a body.

Slope of line

Hence

Second Equation Of Motion:

In speed-time graph, the total distance S travelled by the body is equal to the total area OABD under the graph. That is

Third Equation Of Motion:

In speed-time graph shown in figure 2.26, the total distance S travelled by the body is given by the total area OABD under the graph.

2.14 Sketch a velocity – time graph for the motion of the body. From the graph explaining each step, calculate total distance covered by the body.

Unit 3

Q Differentiate between kinematics and dynamics.

Sr.	*Kinematics*	*Dynamics*
1.	Kinematics is the study of motion of an object without discussing the causes of motion.	The branch of mechanics that deals with the study of motion of an object and in which we study the cause of its motion is called dynamics.
2.	In kinematics motion of body is studies without the reference of mass and force.	In dynamics motion of body is studied with the reference of mass and force.

Q What is force?

A force moves or tends to move, stops or tends to stop the motion of a body. The force can change the direction of motion of a body

Example:

Pushing a door to open and close requires force.

Q What happens when you press a balloon?

Balloon is filled with air. When we apply force on a balloon it change the shape or size of balloon.

Q What is inertia?

Inertia of a body is its property due to which it resists any change in its state of rest or motion.

Example:

If we are sitting in a car. Then on application of brakes our body moves in forward direction due to inertia.

Q A bullet has a very small inertia due to its small mass but why does its impact is so strong when it is fired from the gun?

When a bullet is fired from gun, it possesses momentum. As the speed of bullet is very fast as compare to its size so it has large momentum and due to which it has a strong impact when it hit something.

Q What is momentum?

Definition:

Momentum of a body is the quantity of motion it possesses due to its mass and velocity.

Mathematically:

The momentum P of a body is given by the product of its mass m and velocity v. Thus

Quantity:

Momentum is a vector quantity.

Unit:

Its SI unit is kgms^-1.

Q State Newton First Law of Motion.

Statement:

A body continues its state of rest or of uniform motion in a straight line provided no net force acts on it.

Q Why Newton First Law of Motion is also known as law of inertia?

Law state that a body continues its state of rest or of uniform motion in a straight line provided no net force acts on it.Since Newton’s first law of motion deals with the inertial property of matter. Therefore, Newton’s first law of motion is also known as law of inertia.

Q When driver apply brakes of bus, why passenger fall forward?

The passengers standing in a bus fall forward when its driver applies brakes suddenly. It is because the upper parts of their bodies tend to continue their motion, while lower parts of their bodies in contact with the bus stop with it. Hence, they fall forward.

Q State and explain second law of motion.

Newton’s second law of motion:

Statement:

When a net force acts on a body, it produces acceleration in the body in the direction of net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportion to its mass.

Formula:

F = ma

Proof:

If a force produces an acceleration “a” in a body of mas “m” then we can state mathematically that.

Replacing sign of proportionality

In SI Units, the value of k comes out to be 1.

Hence,

F = ma

One Newton:

The SI unit of force is newton (N).

Definition:

One newton (1N) is the force that produces an acceleration of 1ms^–2 in a body of mass 1 kg.

Mathematically:

1N = 1kg × 1ms^–1

Or 1N = 1kgms^–2

Q State third law and give examples.

Statement:

To every action, there is always an equal but opposite reaction.

Example:

A book laying on a table:

The weight of the book is acting on the table in the downward direction. This is the action. The reaction of the table acts on the book in the upward direction.

A rocket:

A rocket moves on the same principal. When its fuel burns, hot gases escape out from its tail with a very high speed. The reaction of these gases on the rocket causes it to move opposite to the gases rushing out of its tail.

Q Stretch out your palm and hold a book on it.

1. How much force you need to prevent the book from falling?

2. Which is action?

3. Is there any reaction? If yes, then what is its direction?

1. To prevent the book from falling a force equal to weight is needed.

2. The weight of the book is action.

3. “To every action, there is always an equal but opposite reaction.” From Newton third law of motion it is clear that hand apply reaction. Direction of weight is in downward direction so reaction force is in upward direction.

Q Define tension in a string.

Consider block supported by a string. Upper end of the string is fixed on a stand. Let w be the weight of the block. The block pulls the string downwards by its weight. This causes a tension T in the string. The tension T in the string acting upward at the block. As the block is at rest, therefore, the weight of the block acting downwards must be balanced by the upwards tension T in the string. Thus, tension T in the string must be equal and opposite to the weight w of the block.

Q Calculate the tension in the string and acceleration produces in the moving bodies when two bodies connected by the string that passes over the frictionless pulley?

Consider two bodies A and B of masses m₁ and m₂ respectively. Let m₁ is greater than m₂. The bodies are attached to the opposite ends of an inextensible string. The string passes over a frictionless pulley as show in figure.

The body “A” being heavier must be moving downward with some acceleration. Let this acceleration “a”. At the same time, the body “B” attached to the other end of the string moves up with the some acceleration “a”.

As the pulley is frictionless, hence, tension will be the same throughout the string. Let the tension in the string be “T”.

Net Force acting on Body “A”

As the body A is moving downward so,

Net force = larger force – smaller force

According to Second law of motion

So,

………(i)

Net force acting on body “B”

As the body is B is moving upward

So,

Net force = Large fore – smaller force

According to Second law of motion

So,

………(ii)

Calculation of Acceleration:

By adding equation (i) and (ii)

Calculation of Tension:

Putting the value of acceleration in equation (ii)

Q Calculate tension in the string and acceleration produced in the moving bodies when two bodies attached to the ends of the string that passes over the frictionless pulley such that one body moves vertically and the other moves a smooth horizontal surface?

Consider two bodies A and B of masses m₁and m₂ respectively to the ends of an inextensible string as show in figure. Let the body a moves downward with an acceleration a. Since the string is inextensible therefore, body B also moves over the horizontal surface with the same acceleration a. as the pulley is frictionless, hence tension T will be the same throughout the string.

Net force acting on body “A”

As the body A is moving downward

So,

Since body A moves downward, therefore, its weight m1 g is greater than the tension T in the string.

F = m₁g – T

According to second law of motion

F = ma

So,

m₁a = m₁g – T ……….. (i)

Net force acting of “B”

The force acting on body “B” is:

Weight m₂g of the body to acting downward.
Reaction R of the horizontal surface action of body “B” in the upward direction.
Tension “T” in the string pulling the body “B” horizontal over the smooth surface.

As body B has no vertical motion, hence resultant of vertical forces (m₂g and R) must be Zero.

As the body “B” is moving upward so,

Net force = T

F = T

According to motion:

F = ma

So, m₂a = T ………(ii)

Calculation of Acceleration:

Putting the value of tension in equation (i)

Calculation of Tension

Putting the value of acceleration in equation (ii)

Q What is an Atwood’s machine?

Atwood Machine:

An Atwood machine is an arrangement of two objects of unequal masses attached the ends of a string and the string passes over a frictionless pulley. This is used to find the acceleration due to gravity.

Formula:

Q Prove that kgms^-1 = N.s.

As we know that one Newton is equal to kilogram meter per second per second (kgms^-2).

Multiplying both sides by “s” we get

Q Why fragile objects are packed with Styrofoam rings?

Fragile objects such as glass waves etc. are packed with suitable materials such as Styrofoam rings, balls, polythene sheets with air sacks etc.

Air enclosed in the cavity of these materials makes them flexible and soft. During any mishap, the increase the impact time on fragile objects. An increase in impact time lowers the rate of change of momentum and hence lessens the impact of force. This lowers the possible damage due to an accident.

Q Why vehicles have rigid cages for passengers?

In an accident at high speed, the impact force is very large due to the extremely short stopping time. For safety purposes, vehicles have rigid cages for passengers with crumple zones at their front and rear ends.

During an accident, crumple zones collapse. This increases the impact time by providing extra time for crumpling. Impact of force is highly reduced and saves the passengers from severe injuries.

Q How seat belts are useful?

Seatbelts are useful in two ways:

They provide an external force to a person wearing seatbelt.
The additional time is required for stretching seat belts. This prolongs the stopping time for momentum to change and reduces the effect of collision.

Q What is isolated system?

“An isolated system is a group of interacting bodies on which no external force is acting”.

Q What are the applications of law of conservation of momentum?

Application of Law of Conservation of Momentum:

Law of conservation of momentum is very important because it is applicable on all objects in the universe either larger or smaller. This law has vast applications. According to this law, the momentum of an isolated system of two or more than two interacting bodies remains same.

Recoil of Gun:

Consider a system of gun and bullet. Before firing the gum, both the gun and bullet are at rest, so the total momentum of the system is zero. As the gun is fired, bullet shoots out of the gun and acquire momentum. To conserve momentum of the system, the gun recoils. According to the law of conservation of momentum, the total momentum of the gun and the bullet will be zero after the gum fired. Let m be the mass of the bullet and v be its velocity on firing the gun; M be after the mass of the gun and V be the velocity with which it recoils. Thus the total momentum of the gun and the bullet after the gun is fired will be;

According to the law of conservation of momentum:

[Total momentum of the system before firing] = [ Total momentum of the system after firing]

Hence

Equation gives the velocity vof the gun. Negative sign indicates that velocity of the gun is opposite to the velocity of the bullet i.e., the gun recoils. Since mass of the gun is much larger than the bullet, therefore the recoil is much smaller than the velocity of the bullet.

Rockets and jet engines:

Rockets and Jet Engines work on the law of conservation of momentum. In these machines, hot gases produced by burning of fuel such out with large momentum. The machines given an equal and opposite momentum. This enables then to move with very high velocities.

Q Why a moving ball stops?

A force not only moves an object but also stops moving object.Naturally there are some force likefriction, air resistance, or gravity that stops moving objects. When ball move and touches with ground these forces slow down the speed of a ball at the end ball stops moving.

Q Why bicycle stops when the cyclist stops pedalling?

A force not only moves an object but also stops moving object.Naturally there are some force likefriction, air resistance, or gravity that stops moving objects. When tyres of bicycle move and touches with ground these forces slow down the speed of a bicycle at the end bicycle stops moving.

Q Define friction. Describe its cause and explain its different types.

Force of Friction:

Definition:

The force that opposes the motion of moving objects is called friction.

Unit:

Its SI Units is Newton.

Direction:

It is always opposite to the direction of motion.

Dependence:

Frictional force depends upon the following factors.

Nature of surfaces in contacts each other.
Normal force or pressing force.

Cause of friction:

No surface is perfectly smooth. A surface that appears smooth has pits and bumps that can be seen under a microscope. A magnified view of two smooth surfaces in contact shows the gaps and contact between them. The contact points between the two surfaces from a sort of cold welds. These welds resist the surface from sliding over each other.

Types:

There are following types of friction:

Static Friction.
Limiting Friction.
Kinetic Friction.
Sliding Friction.
Rolling Friction.

Static Friction:

The resisting force between the two surfaces before the motion starts is called static friction. It is denoted by F_S.

Limiting Friction:

The maximum value of friction is called liming friction. It denoted by F_S.

Kinetic Friction:

The fore of friction that operates during the movement is called kinetic friction. It is denoted by F_k.

Sliding Friction:

This is the friction produced by sliding the surfaces of one object on the other is called rolling friction.

Rolling Friction:

The force that resists the motion of a body rolling on a surface is called rolling friction.

Derivation:

Limiting friction increases with the increase in normal force. So,

Where µ is called as co-efficient of friction.

Coefficient of Friction:

The ration between the force of limiting friction FS and normal reaction R is constant. This constant is called coefficient of friction.

Formula:

Units:

Because it is the ratio of two forces, so it has “No unit”

Q On what principal rockets and jets engines work? Explain.

Rockets and Jet Engines:

Rockets and Jet Engines work on the law of conservation of momentum. In these machines, hot gases produced by burning of fuel such out with large momentum. The machines gain an equal and opposite momentum. This enables them to move with very high velocities.

Q What are cold welds?

Cold Welds:

The contact points between the surfaces are called cold welds.

Explanation:

A magnified view of two smooth surfaces in contact shows the gaps and contacts between them. The contact points between the two surfaces from a sort of cold welds. These cold welds resist the surfaces from sliding over each other.

Q Define co-efficient of friction. Write its formula and units.

Co-efficient of Friction:

The ratio between the force of limiting friction Fs and normal reaction R is constant. This constant is called coefficient of friction.

Formula:

Units:

Because it is the ratio of two forces so it has “no unit”

Q Write any four advantages of friction.

Advantages of Friction:

Some of the advantages of friction are:

We cannot write if there would be no friction between paper and pencil.
Friction enables us to walk on ground. We cannot run on a slippery ground because it offers very little friction.
Birds could not fly, if these are no air resistance. The reaction of pushed air enables the birds to fly.
Friction is highly desirable when climbing up a hill.
A nail can stay in wood due to friction.

Q Give some disadvantages of friction.

Disadvantages of friction:

Some of the disadvantages of friction are:

Friction is undesirable when moving with high speeds because opposes the motion and thus limits the speed of moving objects.
Most of our useful energy is lost as heat and sound due to the friction between various moving parts of machine.
Due to friction machine catch fire.

Friction produces heat in various parts of the machine.
Friction decreases the efficiency of the machine.
Friction causes wear and tear in the machines.
Friction reduces the speed of moving vehicles largely.

Q Why athletes use special shoes that have extraordinary ground grip?

Friction is needed to walk on the ground. Athletes use special shoes that have extraordinary ground grip. Such shoes prevent them from slipping while running fast.

Q What will we do to stop our bicycle?

We will apply brakes. The rubber pads pressed against the rims provide friction. It is the friction that stops the bicycle.

Q Which shoe offer less friction?

Shoes which have smooth soles offer less friction.

Q Which shoe is better for walking on dry track?

Shoes which have smooth solesis better for walking on dry track.

Q Which shoe is better for jogging?

Shoes that have extraordinary ground gripis better for jogging.

Q Which sole will wear out early?

Shoes which have smooth soleswill wear out early.

Q Why is it easy to roll a cylindrical eraser on a paper sheet than to slide it?

It is easy to roll a cylindrical eraser on a paper sheet than to slide it because the area of contact of eraser in rolling is less than the area of contact of eraser in sliding.

Q Do we roll or slide the eraser to remove the pencil work from our notebook?

We slide the eraser to remove the pencil work from our notebook.

Q In which case do you need smaller force and why?

i. Rolling

ii. Sliding

In case of rolling object we need smaller force because in rolling object less area is in contact.

Q In which case it is easy for the tyre to roll over?

i. Rough ground

ii. Smooth ground

In case of smooth ground it is easy to roll over the tyre because smooth surface offer less friction.

Q Why friction is reduced when tyre rolls rather than to slide?

When the axle of a wheel is pushed, the force of friction between the wheel and the ground at the point of contact provides the reaction force. The reaction force acts at the contact points of the wheel in a direction opposite to the applied force. The wheel rolls without rupturing the cold-welds. That is why the rolling friction is extremely small than sliding friction.

Q Why threading on tyre is necessary?

The wheel would not roll on pushing it if there would be no friction between the wheel and the ground. Thus, friction is desirable for wheels to roll over a surface. It is dangerous to drive on a wet road because the friction between the road and the tyres is very small. This increases the chance of slipping the tyres from the road. The threading on tyres is designed to increase friction. Thus, threading improves road grip and make it safer to drive even on wet road.

Q What a cyclist do to stop his/her bicycle?

A cyclist applies brakes to stop his/her bicycle. As soon as brakes are applied, the wheels stop rolling and begin to slide over the road. Since sliding friction is much greater than rolling friction. Therefore, the cycle stops very quickly.

Q What are the velocity components of the moving wheels of a vehicle?

The wheels of a moving vehicle have two velocity components:

Motion of wheels along the road.
Rotation of wheels about their axis.

Q What is skidding of vehicles?

To stop a car quickly, a large force of friction between the tyres and the road is needed. But there is a limit to this force of friction that tyres can provide. If brakes are applied too strongly, car wheels stop turning and car will skid (lose directional control) due to its large momentum.

Q Why friction is undesirable?

Friction is undesirable when moving at high speeds because it opposes the motion and thus limits the speed of moving objects. Most of our useful energy is lost as heat and sound due to the friction between various moving parts of machines. In machines, friction also causes wear and tear of their moving parts.

Q Why it is dangerous to walk on a slippery ground?

We cannot run on a slippery ground. A slippery ground offers very little friction. Hence, anybody who tries to run on a slippery ground may meet an accident.

Q What is centripetal force? Also derive its expression.

Centripetal Force:

Definition:

Centripetal force is a force that keeps a body to move in a circle.

Formula:

Direction:

It is always directed toward the centre of the circle.

Explanation:

Consider a body tied at the end of a string moving with uniform speed in a circular path. A body has the tendency to move in a straight line due to inertia. The string to which the body is tied keeps it to move in a circle by pulling the body towards the centre of the circle. The string pulls the body perpendicular to its motion as show in figure. This pulling force continuously changes the direction of motion and remains towards the centre of the circle. This centre seeking force is called centripetal force. It keeps the body to move in a circle centripetal force always acts perpendicular to the motion of the body.

Derivation:

Let a body of mass “m” moves with uniform speed “v” in a circle of radius “r” as show in figure. Greater the mass of object greater the centripetal force required

So,

……(i)

Greater the velocity of object greater the centripetal force required. So,

……..(ii)

Lesser the radius of circle greater the centripetal force required. So,

Combining equation (i), (ii) and (iii)

In SI units the value of constant is equal to 1, so

Q What is Centripetal Acceleration? Also derive its expression.

Centripetal Acceleration:

The acceleration produced by the centripetal force called as centripetal acceleration.

Direction:

It is always directed towards the centre of the circle.

Formula:

According to Newton’s second law of motion.

Putting the value of centripetal force (F_C) in above equation:

Q Define Centripetal force. Also give two examples.

Definition:

Centripetal force is a force that keeps a body to move in a circle.

Example:

i. A stone tied to one end of a string rotating in a circle. The tension in the string provides the necessary centripetal force. It keeps the stone to remain in the circle. If the string is not strong enough to provide the necessary tension, it breaks and the stone moves away along a tangent to the circle.

ii. The moon revolves around the Earth. The gravitational force of the Earth provides the necessary centripetal force.

Q On what factors centripetal force depends?

Equation shows that the centripetal force depends on:

Mass
Velocity
Radius

Q Define centrifugal force.

According to Newton third law of motion, every action have equal reaction but opposite in direction. Centrifugal force is the reaction force of centripetal force.

Direction:

It is always directed out wards to the center of the circle.

Q On which principle coaster cars work?

While the coaster cars move around the loop, the track provides centripetal force preventing them to move away from the circle.

Q What is meant by banking of road?

The car would skid if the force of friction between the tyres and the road is not sufficient enough particularly when roads are wet. This problem is solved by banking of curved roads. Banking of a road means that the outer edge of a road is raised. It causes a components of vehicle’s weight to provide necessary centripetal force while taking a turn.

Q How washing machine dryer work?

The dryer of a washing machine is basket spinners. They have a perforated wall having large numbers of fine holes in the cylindrical rotor. The lid of the cylindrical container is closed after putting wet clothes in it. When it spins at high speed, the water from wet clothes is forced out through these holes due to lack of centripetal force.

Q What is a Cream separator?

Most modern plants use a separator to control the fat contents of various products. A separator is a high-speed spinner. It acts on the same principle of centrifuge machines. The bowl spins at very high speed causing the heavier contents of milk to move outward in the bowl pushing the lighter contents inward towards the spinning axis. Cream or butterfat is lighter than other components in milk. Therefore, skimmed milk, which is denser than cream is collected at the outer wall of the bowl. The lighter part (cream) is pushed towards the centre from where it is collected through a pipe.

Exercise

3.1 Encircle the correct answer from the given choices.

b	c	c	a	d	b
c	d	d

3.2 Define the following terms:

i. Inertia:

Inertia of a body is its property due to which it resists any change in its state of rest or motion.

Example:

If we are sitting in a car. Then on application of brakes our body moves in forward direction due to inertia.

ii. Momentum:

Definition:

Momentum of a body is the quantity of motion it possesses due to its mass and velocity.

Mathematically:

The momentum P of a body is given by the product of its mass m and velocity v. Thus

Quantity:

Momentum is a vector quantity.

Unit:

Its SI unit is kgms^-1.

iii. Force:

A force moves or tends to move, stops or tends to stop the motion of a body. The force can change the direction of motion of a body

Example:

Pushing a door to open and close requires force.

Force of friction:

Definition:

The force that opposes the motion of moving objects is called friction.

Unit:

Its SI Units is Newton.

Direction:

It is always opposite to the direction of motion.

Dependence:

Frictional force depends upon the following factors.

Nature of surfaces in contacts each other.
Normal force or pressing force.

Centripetal force:

Centripetal force is a force that keeps a body to move in a circle.

Formula:

Direction:

It is always directed toward the centre of the circle.

3.3 What is the difference between:

i. Mass and weight.

*Sr.*	*Mass*	*Weight*
1.	Mass of body is the quantity of matter that it possesses.	Weight of a body is equal to the force with which earth attracts the body towards its center.
2.	Mass is scalar quantity.	Weight is a vector quantity.
3.	Mass is measured by physical balance.	Weight is measured by spring balance.
4.	Mass of body remains uniform everywhere.	Weight of body varies depending upon the value of “g”.
5.	Its formula is m = F/a	Its formula is w = mg.
6.	Its SI unit is kilogram.	Its SI unit is Newton.

ii. Action and reaction.

*Sr.*	*Action*	*Reaction*
1.	A force that is exerted by 1^st body on the 2^nd body is called action.	A force that is exerted by 2^nd body on the 1^st body is called reaction.
2.

iii. Sliding friction and rolling friction.

*Sr.*	*Sliding Friction*	*Rolling Friction*
1.	A force between the sliding objects which opposes the relative motion between then is called sliding friction.	The force of friction between a rolling body and the surfaces over which it rolls is called rolling friction.
2.	Contact area is large in it.	Contact area is less in it.
3.	Sliding friction is more than rolling friction.	Rolling friction is less than sliding friction.

3.4 What is the law of inertia?

Newton’s first law of motion deals with the inertial property of matter, therefore, Newton’s first law of motion is also known as law of inertia which states that:

“A body continues its state of rest or of uniform motion in straight line provided no net force acts on it.”

3.5 Why is it dangerous to travel on the roof of a bus?

The friction or drag force due to air acting on the upper part of the body of a person standing on the roof of running bus tries to turn over which is dangerous while the lower part of body remains at rest with respect to roof of the bus.

3.6 Why does a passenger move outward when bus takes a turn?

When a bus takes a sharp turn, passengers fall in the outward direction. It is due to inertia that they want to continue their motion in a straight line and thus fall outwards.

3.7 How can you relate a force with the change of momentum of a body?

Relation between force and momentum:

When a force acts on a body, it produces acceleration in the body and will be equal to the rate of change of momentum of the body.

Derivation

Suppose a force “F” increases the velocity of a body of mass “m” form “v_i” to “v_f” during the time “t”.

Then,

Thus the rate of change in momentum is given by

As,

According to Newton’s second law of motion.

Rate of change in momentum = Applied force

Equation also defines force and states Newton’s second law of motion as

When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

SI unit of momentum defined by equation is newton-second (Ns) which is the same as kgms^-1.

3.8 What will be the tension in the rope that is pulled from the end by twoopposite forces 100N each?

When two forces of 100 N each applied on a string then resultant tension isequal to 100.

3.9 Action and reaction are always equal and opposite. Then how does a body moves.

If one body apply action on some another object, then object give equal and opposite reactional force to the body. Action and reaction are equal in magnitude but opposite in direction. Action and reaction do not act on the same body. Due to which body moves.

3.10 A horse pushes the cart. If the action and reaction are equal and opposite, then how does the cart move?

If horse, apply action force on road, then road give equal and opposite reactional force to the horse. Action and reaction are equal in magnitude but opposite in direction. Action and reaction do not act on the same body. Due to which horse moves. As cart tied with horse, so cart moves with horse.

3.11 What is the law of conservation of momentum?

Statement:

The momentum of an isolated system of two or more than two interacting bodies remains same.

Mathematical Expression:

Isolated system:

An isolated system is a group of interacting bodies on which no external force is acting.

Derivation:

Consider an isolated system of two spheres masses m₁ and m₂ as shown in figure.

They are moving in a straight line with initial velocities u₁and u₂respectively, such that u₁is greater than u₂. Sphere of mass m₁ approaches the sphere of mass m₂ as they more. After sometime mass m₁ hits m₂ with some force.

According to Newton’s third law of motion m₁ exerts an equal and opposite reaction force on m₁. Let their velocities become v₁ and v₂ respectively after collision.

Total Momentum before collision:

Also;

Total Momentum after collision:

Also;

Hence,

According to the law of conservation of momentum

[Total momentum of the system before collision] = [total momentum the system after collision]

3.12 Why is the law of conservation of momentum important?

With the help of using law of conservation of momentum it is possible to calculate, force, velocity, acceleration of a body. Most of elementary particles were discovered bythis law.

3.13 When a gun is fired it recoils why?

Consider a system of a gun and a bullet. Before firing the gun, both the gun and bullet are at rest, so the total momentum of the system is zero. As the gun is fired, bullet shoots out of the gun and it acquires momentum. To conserve momentum of the system the gun recoils. As

Negative sign indicates that velocity of gun is opposite to velocity of the bullet i.e. the gun recoils.

3.14 Describe two situations in which force of friction in needed?

Friction is desirable in many conditions. Two of them are given below.

Friction enable us to walk, on the ground. We cannot run on slippery ground. A slippery ground offers very little friction. Hence, anybody who tries to run on slippery ground may meet on accident.
Friction is needed when we write. We cannot write if there would be no friction between paper and pencil.

3.15 How does oiling the moving parts of a machine lowers friction?

Friction is less in smooth objects then in rough objects. Oiling makes objects smoother. That’s why, oiling the moving parts of a machine lowers friction by reducing roughness between the parts of machine.

3.16 Describe ways to reduce friction.

The friction can be reduced by:

Making the sliding surfaces smooth.
Making the fast moving objects a streamline shape (fish shape) such as cars, aeroplanes, etc. This causes the smooth flow of air and thus minimizes air resistance at high speeds.
Lubricating the sliding surfaces.
Using ball bearings or roller bearings .Because the rolling friction is lesser than the sliding friction.

3.17 Why rolling friction is less than sliding friction?

Frictional force depend on area of contact between two surfaces. When an object slides across the ground, it has much more surface area in direct contact with the ground relative to sliding. So rolling friction is less than sliding friction.

3.18 What you know about the following:

i. Tension in a string:

ii. Limiting Friction:

The maximum value of friction is called liming friction. It denoted by FS.

iii. Braking Force:

It can be explained by following two examples. As soon as brakes of cycle are applied, the wheels stop rolling and begin to slide over a road, since sliding friction is much greater than rolling friction. So cycle stops very quickly. In order to reduce the chance of skidding, it is advisable not to apply brakes too hard that lock up their rolling motion especially at high speeds.

iv. Skidding of Vehicle:

To stop a car quickly, a large force of friction between the tyres and the road is needed. But there is a limit to this force of friction that tyres can provide. If the brakes are applied too strongly, the wheels of the car will lock up (stop turning) and the car will skid due to its large momentum. It will lose its directional control that may result in an accident.

Seatbelts:

Seatbelts are the belts connected with the seats of vehicles. It stops the upper part of passengers to move forward due to inertia. Seatbelts are useful in two ways:

They provide an external force to a person wearing seatbelt.
The additional time is required for stretching seat belts. This prolongs the stopping time for momentum to change and reduces the effect of collision.

Banking of Roads:

Cream Separator:

3.19 What would happen if all friction suddenly disappears?

When the frictional force suddenly disappears the motion of the object would never be stopped.

3.20 Why the spinner of a washing machine is made to spin at a high speed?

At very high spinning speed the water and dirt particles are separate from cloths due to lack of centripetal force.

Unit 4

Q What are parallel forces? Name its types.

Parallel Forces:

If a number of forces act on a body such that their points of action are different but lines of action are parallel to each other, these forces are called parallel forces.

Types:

There are two types of parallel forces.

Like parallel forces.
Unlike parallel forces.

Q What are like parallel forces? Also give example.

Like Parallel Forces:

Like parallel forces are the forces that are parallel to each other and have the same direction.

Example:

A bag filled with apples. The weight of the bag is due to the weight of all the apples in it. Since the weight of every apple in the bag is the force of gravity acting on it vertically downwards, therefore, weights of apples are the parallel forces. All these forces are acting in the same direction. Such forces are called like parallel forces.

Q What are unlike parallel forces? Also give example.

Unlike Parallel Forces:

Unlike parallel forces are the forces that are parallel but have directions opposite to each other.

Example:

An apple is suspended by a string. The string is stretched due to weight of the apple. The forces acting on it are; weight of the apple acting vertically downward and tension in the string pulling it vertically upward. The two forces are parallel but opposite to each other. These forces are called unlike parallel forces.

Q How forces are added?

Force is a vector quantity. It has both magnitude and direction; therefore, forces are not added by ordinary arithmetical rules. When forces are added, we get a resultant force. One of the methods for the addition of forces is a graphical method. In this method forces can be added by head to tail rule of vector addition.

Q Define resultant force.

A resultant force is a single force that has the same effect as the combined effect of all the forces to be added.

Q Define head to tail rule.

Head to tail rule:

In order to get the resultant of two or more vectors, draw the representative lines of the given vectors in such a way that the head of one coincides with the tail of other. The straight line is draw by joining the tail of first vector to the head of the last one; give the resultant vector of these vectors. The direction of this resultant vector is directed from tail of first vector to the head of last one. This method is known as head to tail rule of vector addition.

Q In a right angled triangle length of base is 4cm and its perpendicular is 3 cm. Find

Length of hypotenuse

== = 0.6

== = 0.8

== = 0.75

Q Define rigid body.

A body is composed of large number of small particles. If the distances between all pairs of particles of the body do not change by applying a force then it is called a rigid body. In other words, a rigid body is the one that is not deformed by force or forces acting on it.

Q Define axis of rotation.

Consider a rigid body rotating about a line. The particles of the body move in circles with their centers all lying on this line. This line is called the axis of rotation of the body.

Q Explain torque. On what factors it depend?

Torque:

The turning effect of a force is called torque or moment of the force.

Line of Action of a Force:

The line along which a force acts is called the line of action of the force.

Moment Arm:

The perpendicular distance between the axis of rotation and the line of action of the force is called the moment arm of the force. Represented by L.

Mathematically:

τ = F × L

Dependence:

The torque or moment of a force depends upon the:

Force F
Moment arm L

Unit:

SI unit of torque is newton-metre (Nm).

Q Why the handle of a door is fixed near the outer edge of a door?

The door rotates about the hinges, due to torque. The torque depends upon the force and moment arm of the force. When the handle of a door is fixed near the outer edge of a door its moment arm increases. We can open or close a door more easily by applying a force at the outer edge of a door rather than near the hinge.

Q It is easy to tighten a nut using a spanner of longer arm than a spanner of shorter arm?

The torque depends upon the force and moment arm of the force. The moment produced by a force using a spanner of longer arm is greater than the torque produced by the same force but using a spanner of shorter arm. A spanner having long arm helps to tighten a nut with greater ease than the one having short arm.

Q A force of 150 N can loosen a nut when applied at the end of a spanner 10 cm long.

What should be the length of the spanner to loosen the same nut with a 60 N force?

As,

2. How much force would be sufficient to loosen it with a 6 cm long spanner?

Q State principle of moments.

A body is balanced if the sum of clockwise moments acting on the body is equal to the sum of anticlockwise moments acting on it.

Q Define clockwise moment and anticlockwise moment.

Clockwise Moment:

A force that turns a spanner in the clockwise direction is generally used to tighten a nut. The torque or moment of the force so produced is called clockwise moment.

Anticlockwise Moment:

To loosen a nut, the force is applied such that it turns the nut in the anticlockwise direction. The torque or moment of the force so produced is called anticlockwise moment.

Q Can a small child play with a fat child on the see saw? Explain how?

Yes, a small child play with a fat child on the see saw. A fat boy can play with small child by reducing its moment arm.

Q Two children are sitting on the see-saw, such that they can not swing. What is the net torque in this situation?

When two children are sitting on the see-saw, such that they can not swing. The net torque in this situation will be zero.

Q Define centre of mass.

Centre of mass of a system is such a point where an applied force causes the system to move without rotation.

Q Does the system move without rotation if the force acts other than centre of mass?

Consider a system of two particles A and B connected by a light rigid rod as shown in figure. Let O is a point anywhere between A and B such that the force F is applied at point O as shown in figure. If the system moves in the direction of force F without rotation, then point O is the centre of mass of the system.

1. Let the force be applied near the lighter particle as shown in figure. The system moves as well as rotates.

2. Let the force be applied near the heavier particle as shown in figure. In this case, also the system moves as well as rotates.

Conclusion:

Centre of mass is the only point of a system where an applied force causes the system to move without rotation.

Q Define centre of gravity.

A point where the whole weight of the body appears to act vertically downward is called centre of gravity of a body.

Q Find centre of gravity of symmetrical objects?

Rod	The centre of gravity of a uniform rod lies at a point where it is balanced. This balance point is its middle point G
Square	The centre of a gravity of a uniform square sheet is the point of intersection of its diagonals.
Circular Disc	The centre of gravity of a uniform circular disc is its centre.
Rectangle	The centre of a gravity of a uniform rectangular sheet is the point of intersection of its diagonals.
Triangular Sheet	The centre of gravity of a uniform triangular sheet is the point of intersection of its medians.
Circular Ring	The centre of gravity of a uniform circular ring is the centre of the ring.
Hollow Cylinder	The centre of gravity of a uniform solid or hollow cylinder is the middle point on its axis.

Q How we can find centre of gravity of an irregular shaped thin lamina?

A simple method to find the centre of gravity of a body is by the use of a plumbline. A plumbline consists of a small metal bob (lead or brass) supported by a string. When the bob is suspended freely by the string, it rests along the vertical direction due to its weight acting vertically downward. In this state, centre of gravity of the bob is exactly below its point of suspension.

Q Find centre of gravity of an irregular piece of cardboard.

Take an irregular piece of cardboard. Make holes A, B and C as shown in figure near itsedge. Fix a nail on a wall. Support the cardboard on the nail through one of the holes (let it be A), so that the cardboard can swing freely about A. The cardboard will come to rest with its centre of gravity just vertically below the nail. Vertical line from A can be located using a plumbline hung from the nail. Mark the line on the cardboard behind the plumbline. Repeat it by supporting the cardboard from hole B. The line from B will intersect at a point G. Similarly, draw another line from the hole C. Note that this line also passes through G. It will be found that all the vertical lines from holes A B and C have a common point G. This Common point G is the centre of gravity of the cardboard.

Q Define couple and also give its examples.

Definition:

A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.

Examples:

A double arm spanner
Steering wheel

Explanation:

A double arm spanner is used to open a nut. Equal forces each of magnitude Fare applied on ends A and B of a spanner in opposite direction as shown in figure. These forces form a couple that turns the spanner about point O. The torques produced by both the forces of a couple have the same direction. Thus, the total torque produced by the couple will be:

Equation gives the torque produced by a couple of forces F and F separated by distance AB. The torque of a couple is given by the product of one of the two forces and the perpendicular distance between them.

Q How wheel of the bicycle rotate?

A cyclist pushes the pedals of a bicycle. This forms a couple that acts on the pedals. The pedals cause the toothed wheel to turn making the rear wheel of the bicycle to rotate.

Q Define equilibrium and its conditions with the help of examples.

Equilibrium:

A body is said to be in equilibrium if no net force acts on it.

Examples:

A book lying on a table.
A picture hanging on a wall.

Explanation:

Consider a log of wood of weight w supported by ropes as shown in figure. Here the weight w is balanced by the forces F₁ and F₂ pulling the log upward. In case of objects moving with uniform velocity, the resultant force acting on them is zero.

Conditions for Equilibrium:

There are two conditions for equilibrium.

First Condition for Equilibrium:

A body is said to satisfy first condition for equilibrium if the resultant of all the forces acting on itis zero.

Let n number of forces F₁, F₂, F₃,………..,F_n are acting on a body such that,

The symbol is a Greek letter called sigma used for summation.

The first condition for equilibrium can also be stated in terms of x and y-components of the forces acting on the body as:

And,

Examples:

A book lying on a table.
A picture hanging on a wall.
A paratrooper coming down with terminal velocity.

Second Condition for Equilibrium:

A body satisfies second condition for equilibrium when the resultant torque acting on it is zero.

Examples:

A ladder leaning at a wall.
A ceiling fan rotating at constant speed.

Q A ladder leaning at a wall as is in equilibrium. How?

A ladder leaning at a wall as is in equilibrium, because torque acting on it is zero. It satisfies second condition of equilibrium.

Q The weight of the ladder produces an anticlockwise torque. The wall pushes the ladder at its top end thus produces a clockwise torque. Does the ladder satisfy second condition for equilibrium?

Yes, the ladder satisfy second condition for equilibrium because anticlockwise torque and clockwise torque are equal in magnitude but opposite in direction. Hence resultant torque acting on ladder is zero.

Q Does the speed of a ceiling fan go on increasing all the time?

No, the speed of a ceiling fan does not go on increasing all the time. When a fan attains a maximum speed its rotation become constant.

Q Does the fan satisfy second condition for equilibrium when rotating with uniform speed?

A ceiling fan rotating at constant speed is in equilibrium as net torque acting on it is zero.

Q Define states of equilibrium with the help of examples.

There are three states of equilibrium.

Stable Equilibrium:

A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.

Example:

Consider a book lying on the table. Tilt the book slightly about its one edge by lifting it from the opposite side. It returns to its previous position when sets free.

Unstable Equilibrium:

If a body does not return to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium.

Example:

Take a pencil and try to keep it in the vertical position on its. Whenever we leave it, the pencil topples over about its tip and falls down.

Neutral Equilibrium:

If a body remains in its new position when disturbed from its previous position, it is said to be in a state of neutral equilibrium.

Example:

Take a ball and place it on a horizontal surface. Roll the ball over the surface and leave it after displacing from its previous position. It remains in its new position and does not return to its previous position.

Q Why vehicles are made heavy at the bottom?

Vehicles are made heavy at the bottom. This lowers their centre of gravity and helps to increase their stability.

Q Why the base of vehicle made wide?

The base of a vehicle is made wide so that the vertical line passing through its centre of gravity should not get out of its base during a turn. So vehicle become more stable.

Q How a toy keeps itself upright after a tilted?

Toy keeps itself upright when tilted. It has a heavy semi-spherical base. When it is tilted, its centre of mass rises. It returns to its upright position at which itscentre of mass is at the lowest.

Exercise

4.1 Encircle the correct answer from the given choices.

b	d	b	d
d	d	c	c

4.2 Define the following.

(i) Resultant Vector

(ii) Torque

(iii) Centre of Mass

(iv) Centre of Gravity

Resultant Vector:

A resultant vector is a single vector that has the same effect as the combined effect of all the vectors to be added.

Torque:

The turning effect of a force is called torque or moment of the force.

Centre of Mass:

Centre of mass of a system is such a point where an applied force causes the system to move without rotation.

Centre of Gravity:

A point where the whole weight of the body appears to act vertically downward is called centre of gravity of a body.

4.3 Differentiate the following:

i. Like and unlike forces.

ii. Torque and couple.

iii. Stable and neutral equilibrium

(i)

Sr.	Like Forces	Unlike Forces
1.	Like parallel forces are the forces that are parallel to each other and have the same direction.	Unlike parallel forces are the forces that are parallel but have opposite direction.

(ii)

Sr.	Torque	Couple
1.	The turning effect of a force is called torque or moment of force.	A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.
2.	To produce a torque we need at least one force.	To produce a couple we needat least two unlike parallel forces.
4.	Example:Turning pencil in a sharpener and turning doorknob.	Example:Steering of wheel, double arm spanner.

(iii)

Sr.	Stable equilibrium	Neutral equilibrium
1.	A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.	If a body remains in its new position when disturbed from its previous position, it is said to be in a state of neutral equilibrium.
2.	On tilting the centre of gravityof body is raised up from its original position.	On distributing the centre of gravityof body remains at the same height, irrespective to its new position.
3.	Example:A book placed on the table horizontally.	Example:The rolling ball.

4.4 How head to tail rule helps to find the resultant of forces?

4.5 How can a force be resolved into its perpendicular components?

Resolution of Forces:

Definition:

Splitting up of a force into two mutually perpendicular components is called resolution of that force.

Component:

A part of vector, which is effect in a particular direction, is called component of vector.

Rectangular components:

Those components, which are mutually perpendicular to each other, are called the rectangular components.

Explanation:

Consider a force “F” represented by line OA making an angle θ with as shown in figure. Draw a perpendicular AB on from A. Now according to head to tail rule OA is the resultant of vectors represented by OB and BA.

Thus,

The component OB and BA are perpendicular to each other. They are called the rectangular components of OA representing force F. Hence OB represents itsand BA represents its . Therefore;

Horizontal component of Force ():

In right angle triangle OBA

Vertical Component of Force ():

In right angle triangle OBA

Magnitude of Resultant Force ()

Apply Pythagoras theorem in right angle triangle OBA

Taking square of root both sides

Direction of resultant force:

In right angle triangle of OBA

Q When a body is said to be in equilibrium?

A body is said to be in equilibrium if no net force acts on it.A body is in equilibrium if:

If the resultant of all the forces acting on it is zero.
The resultant torque acting on it is zero.

Q Explain the first condition for equilibrium.

A body is said to satisfy first condition for equilibrium if the resultant of all the forces acting on itis zero.

Let n number of forces F₁, F₂, F₃,………..,F_n are acting on a body such that,

The symbol is a Greek letter called sigma used for summation.

The first condition for equilibrium can also be stated in terms of x and y-components of the forces acting on the body as:

And,

Examples:

A book lying on a table.
A picture hanging on a wall.
A paratrooper coming down with terminal velocity.

4.8 Why there is a need of second condition for equilibrium if a body satisfies first condition for equilibrium?

First condition for equilibrium does not ensure that a body is in equilibrium. This is clear from the following example. Consider a body pulled by the forces F₁ and F₂ as shown in figure (a). The two forces are equal but opposite to each other. Both are acting along the same line, hence their resultant will be zero. According to the first condition, the body will be in equilibrium.Now shift the location of the forces as shown in figure (b). In this situation, the body is not in equilibrium although the first condition for equilibrium is still satisfied. It is because the body has the tendency to rotate.

4.9 What is second condition for equilibrium?

A body satisfies second condition for equilibrium when the resultant torque acting on it is zero.

Examples:

A ladder leaning at a wall.
A ceiling fan rotating at constant speed.

4.10 Give an example of a moving body which is in equilibrium.

A paratrooper coming down with terminal velocity (constant velocity) satisfies first condition for equilibrium and is thus in equilibrium.

4.11 Think of a body which is at rest but not in equilibrium.

When a ball thrown vertically upward at its maximum height ball becomes at rest. At this stage ball is at rest but it is not in equilibrium state.

4.12 Why a body cannot be in equilibrium due to single force acting on it?

A body is said to be in equilibrium if no net force acts on it. A single force is not balanced and produces acceleration in the body, thus body cannot be in equilibrium due to a single force.

4.13 Why the height of vehicles is kept as low as possible?

The height of vehicles is kept as low as possible because this lowers the centre of gravity of a car. Stability of a car depends on centre of gravity. By lowering the centre of gravity car attain more stability.

4.14 Explain what is meant by stable, unstable and neutral equilibrium. Give one example in each case.

Stable Equilibrium:

A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.

Example:

Consider a book lying on the table. Tilt the book slightly about its one edge by lifting it from the opposite side. It returns to its previous position when sets free.

Unstable Equilibrium:

If a body does not return to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium.

Example:

Take a pencil and try to keep it in the vertical position on its. Whenever we leave it, the pencil topples over about its tip and falls down.

Neutral Equilibrium:

If a body remains in its new position when disturbed from its previous position, it is said to be in a state of neutral equilibrium.

Example:

Unit 5

Q What is relation between gravitational law and Newton’s third law of motion?

It is to be noted that mass m₁ attracts m₂ towards it with a force F while mass m₁ attracts m₂ towards it with a force of the same magnitude F but in opposite direction. If the force acting on m₁ is considered as action then the force acting on m₂ will be the reaction. The action and reaction due to force of gravitation are equal in magnitude but opposite in direction. This is consistent with Newton’s third law of motion which states, to every action there is always an equal but opposite reaction.

Q What is gravitational field strength?

In the gravitational field of the Earth, the gravitational force per unit mass is called the gravitational field strength of the Earth. At any place its value is equal to the value of g at that point. Near the surface of the Earth, the gravitational field strength is 10 N kg^-1.

Q How can you say that gravitational force is a field force?

Gravitational force is a non-contact force. For example, the velocity of a body, thrown up, goes on decreasing while on return its velocity goes on increasing. This is due to the gravitational pull of the earth acting on the body whether the body is in contact with the earth or not. Such a force is called the field force.

Q What is the value of g at a height equal to one earth radius?

As we know that

When

We come to know that at a height equal to one Earth radius above the surface of the Earth, g becomes one fourth of its value on the Earth.

Q Does an apple attract the Earth towards it?

Yes, an apple attract the Earth towards it because every object attracts every other object but its force of attraction is very small.

Q With what force an apple weighing 1N attracts the Earth?

An apple weighing 1N attracts the Earth with 1N.

Q Does the weight of an apple increase, decrease or remain constant when taken to the top of a mountain?

As we know that,

Value of g decreases with altitude, soweight of an apple decrease when taken to the top of a mountain.

Q On what factors value of g on the surface of a celestial object depends?

Value of g on the surface of a celestial object depends on its mass and its radius, e.g. value of g on Sun is274.2 ms^-2 and on Mercury is 3.7 ms^-2.

Q What is GPS?

Global Positioning System (GPS) is a satellites navigation system. It helps us to find the exact position of an object anywhere on the land, on the sea or in the air. GPS consists of 24 Earth satellites. These satellites revolve around the Earth twice a day with a speed of 3.87 km s^-1.

Q What are satellites? Name their types?

Satellite:

An object that revolves around a planet is called satellite.

Types:

There are mainly two types of satellite:

Natural Satellites
Artificial Satellites

Q Define natural Satellites.

Natural Satellites:

Satellites which naturallyexist in the universe are known as natural satellites.

Example:

The moon revolves around the earth so moon is a natural satellite of earth.

Q What are artificial satellites? Write some of their uses?

Artificial Satellites:

Scientists have sent many objects into space. Some of these objects revolve around the earth. These are called artificial satellites:

Uses:

Artificial satellites are used for:

Word wide communication
Weather observation
Navigation Purposes
Military Purposes

Q What do you know about geostationary orbits?

Geostationary Obits:

Communication satellite takes 24 hours to complete their one revolution around the earth. Earth also completes its one rotation about its axis in 24 hours, hence, this communication satellite to be stationary with respect to earth. It is due to this reason that the orbit of such a satellite is called geostationary orbit.

Q What is orbital velocity also derive its mathematical form.

Orbital Velocity:

It is the velocity of a satellite which moves around the earth at a specific height.

Motion of Artificial Satellite:

A satellite requires centripetal force that keeps it to move around the earth. The gravitational force of attraction between the satellite and the earth provides the necessary centripetal force.

Derivation:

Consider a satellite of mass m revolving around the earth with an altitude of h in an orbit of radius r_owith orbital velocity v_o. The necessary centripetal force required by the satellite is provided by the gravitational force of attraction between the earth and satellite. So,

A satellite revolving around very close to the Earth,has speed v_o nearly 8 kms^-1or 29000 kmh^-1.

Q Differentiate between g and G

g	G
It is acceleration due to gravity.	It is Universal constant of gravitation.
Varies from place to place.	It is constant everywhere.
Its value is 10ms^-2	Its value is 6.673 x 10^-11Nm²kg^-2
Its unit is ms^-2	Its unit is Nm²kg^-2

Exercise

5.1 Encircle the correct answer from the given choices.

Q What is meant by the force of gravitation?

Everybody in the universe attracts every other body with a force. This force of attraction between two bodies is called force of gravitation.

Q Do you attract the Earth or the Earth attracts you? Which one is attracting with a larger force? You or the Earth.

According to Newton’s law of gravitation everybody in the universe attracts every other body with a force. So, we attract the earth and earth also attracts us. Earth is attracting with a larger force due to larger mass.So we moves towards the earth.

Q What is a field force?

Q Why earlier scientists could not guess about the gravitational force?

Gravitational force is the weakest force due to small value of G, the gravitational force of attraction between objects is very small soearlier scientists could not guess about the gravitational force.

Q How can you say that gravitational force is a field force?

Q Explain, what is meant by gravitational field strength?

Q Why law of gravitation is important to us?

Law of gravitation is important to us because:

It is used to calculate force of attraction between two masses.
It is used to calculate mass of the earth.
It is used to calculate mass of the moon.

Q Explain the law of gravitation.

Law of Gravitation:

Statement:

Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Mathematical Expression:

Explanation:

Consider two bodies of masses m₁ and m₂. The distance between the centres of masses is d as show in figure.

Derivation:

According to the law of gravitation the gravitational force of attraction F with which the two masses m₁ and m₂ separated by a distance d attract each other is given by:

Universal Gravitational Constant:

Definition:

It is equal to the force of gravitation between the two objects having mass 1 kg each and separated by a distance of 1 meter.

Value:

Its value is same everywhere. It is unit its value is6.673 × 10^–11 Nm²Kg^–2 .

Q How the mass of Earth can be determined?

Consider a body of mass m on the surface of the Earth as shown in figure. Let the mass of the Earth be Me and radius of the Earth be R. The distance of the body from the centre of the Earth will also be equal to the radius R of the Earth. According to the law of gravitation, the gravitational force F of the Earth acting on a body is given by:

But the force with which Earth attracts a body towards its centre is equal to its weight w. Therefore,

Me = 6.0 × 1kg

Thus, the mass of equation is approximately equal to 6.0 × 1kg.

Q Can you determine the mass of our moon? If yes, then what you need to know?

Yes, mass of moon can be determined by Newton’s Law of gravitation, using the formula:

M_m =

We determine mass of moon if we know:

R_m = Radius of moon
g_m = Value of gravitational acceleration on moon
G = Universal Constant of gravitation. i.e. equal to 6.673 x 10-11 Nm²Kg^-2

Q Why does the value of g vary from place to place?

Equation shows that the value of acceleration due to gravity g depends on the radius of the Earth at its surface. The value of g is inversely proportional to the square of the radius of the Earth. But it does not remain constant. It decreases with altitude. Altitude is the height of an object or place above sea level. The value of g is greater at sea level than at the hills.

Q Explain how the value of g varies with altitude.

Consider a body of mass m at an altitude h as shown in figure. The distance of the body from the centre of the Earth becomes. Therefore, using equation,

we get,

g_h =

According to the above equation, we come to know that at a height equal to one Earth radius above the surface of the Earth, g becomes one fourth of its value on the Earth. Similarly at a distance of two Earths radius above the Earth’s surface, the value of g becomes one ninth of its value on the Earth.

Q What are artificial satellites?

Artificial Satellites:

Scientists have sent many objects into space. Some of these objects revolve around the earth. These are called artificial satellites:

Uses:

Artificial satellites are used for:

Word wide communication
Weather observation
Navigation Purposes
Military Purposes

Q How Newton’s law of gravitation helps in understanding the motion of satellites?

The gravitational force of attraction between the satellite and the earth provides the necessary centripetal force. To move satellite around earth. This force is given by Newton’s Law of gravitation and then by determining its orbital velocity, motion of a satellite can be explained using this equation.

Q On what factors the orbital speed of a satellite depends?

As we know that

So, we can say that orbital speed depends upon:

The gravitation acceleration
Distance between the centre of the earth and satellite

Q Why communication satellites are stationed at geostationary orbits?

Geostationary satellites take 24 hours to complete their one revolution around the earth. As earth also completes its one rotation about its axis in 24 hours. Hence, these geostationary satellites appear to be stationary with respect to earth.

Unit 6

Q A crate is moved by pulling the rope attached to it. It moves 10 m on a straight horizontal road by a force of 100 N. How much work will be done if:

1. The rope is parallel to the road.

As we know that,

When rope is parallel to the road

2. The rope is making an angle of 30° with the road.

As we know that,

When the rope is making an angle of 30° with the road.

Q Define energy write down some forms of energy.

Energy:

A body possesses energy if it is capable to do work.

Forms:

Energy exists in various forms such as mechanical energy, heat energy, light energy, sound energy, electrical energy, chemical energy and nuclear energy etc.

Q Explain different forms of energy.

Energy exists in various forms. Some of the main forms of energy are:

MECHANICAL ENERGY:

The energy possessed by a body both due to its motion or position is called mechanical energy. Water running down a stream, wind, a moving car, a lifted hammer, a stretched bow, a catapult or a compressed spring etc. possess mechanical energy.

HEAT ENERGY:

Heat is a form of energy given out by hot bodies. Large amount of heat is obtained by burning fuel. Heat is also produced when motion is opposed by frictional forces. The foods we take provide us heat energy. The Sun is the main source of heat energy.

ELECTRICAL ENERGY:

Electricity is one of the widely used form of energy. Electrical energy can be supplied easily to any desired place through wires. We get electrical energy from batteries and electric generators. These electric generators are run by hydro power, thermal or nuclear power.

SOUND ENERGY:

Sound is a form of energy. It is produced when a body vibrates; such as vibrating diaphragm of a drum, vibrating strings of a sitar and vibrating air column of wind instruments such as flute pipe etc.

LIGHT ENERGY:

Light is an important form of energy. Plants produce food in the presence of light. We also need light to see things. We get light from candles, electric bulbs, fluorescent tubes and also by burning fuel. However, most of the light comes from the Sun.

CHEMICAL ENERGY:

Chemical energy is present in food, fuels and in other substances. We get other forms of energy from these substances during chemical reactions.

The burning of wood, coal or natural gas in air is a chemical reaction which releases energy as heat and light.

Electric energy is obtained from electric cells and batteries as a result of chemical reaction between various substances present in them.

Animals get heat and muscular energy from the food they eat.

NUCLEAR ENERGY:

Nuclear energy is the energy released in the form of nuclear radiations in addition to heat and light during nuclear reactions such as fission and fusion reactions. Heat energy released in nuclear reactors is converted into electrical energy. The energy coming from the Sun for the last billions of years is the result of nuclear reactions taking place on the Sun.

Q How is energy converted from one form to another? Explain.

Energy cannot be destroyed however it can be converted into some other forms.

For example, when we rub our hands together quickly. We will feel them warm. We have used our muscular energy in rubbing hands as a result heat is produced. In the process of rubbing hands,mechanical energy is converted into heat energy.

Processes in nature are the results of energy changes. For example, some of the heat energy from the Sun is taken up by water to evaporate.

Q What is pole vaulter?

A pole vaulter uses a flexible vaulting pole made of special material. It is capable to store all the vaulter’s kinetic energy while bending in the form of potential energy. The vaulter runs as fast as possible to gain speed. The kinetic energy gained by the pole vaulter due to speed helps him/her to rise up as the vaulter straightens. Thus he attains height as the pole returns the potential energy stored by the vaulter in the pole.

Q What are fossil fuels?

Fossil fuels such as coal, oil and gas to heat our houses and run industry and transport. They are usually hydrocarbons (compounds of carbon and hydrogen). When they are burnt, they combine with oxygen from the air. The carbon becomes carbon dioxide; hydrogen becomes hydrogen oxide called water; while energy is released as heat. In case of coal:

Q Why fossils fuels are called non-renewable form of energy?

The fossil fuels took millions of years for their formation. They are known as non-renewable resources. We are using fossil fuels at a very fast rate. Their use is increasing day by day to meet our energy needs. If we continue to use them at present rate, they will soon be exhausted. Once their supply is exhausted, the world would face serious energy crisis.

Q What are the disadvantages of using fossil fuels?

Fossil fuels release harmful waste products. These wastes include carbon mono-oxide and other harmful gases, which pollute the environment. This causes serious health problems such as headache, tension, nausea, allergic reactions, irritation of eyes, nose and throat. Long exposure of these harmful gases may cause asthma, lungs cancer, heart diseases and even damage to brain, nerves and other organs of our body.

Q Why we need new energy sources for our future?

Fossil fuels would not be able to meet our future energy needs. This would cause serious social and economical problems for countries like us. Therefore, we must use them wisely and at the same time develop new energy sources for our future survival.

Q What are nuclear fuels?

In nuclear power plants, we get energy as a result of fission reaction. During fission reaction, heavy atoms, such as Uranium atoms, split up into smaller parts releasing a large amount of energy. Nuclear power plants give out a lot of nuclear radiations and vast amount ofheat. A part of this heat is used to run power plants while lot of heat goes waste into the environment.

Q Write a note on renewable sources of energy.

Sunlight and water power are the renewable sources of energy. They will not run out like coal, oil and gas.

ENERGY FROM WATER:

Energy from water power is very cheap. Dams are being constructed at suitable locations in different parts of the world. Dams serve many purposes. They help to control floods by storing water. The water stored in dams is used for irrigation and also to generate electrical energy without creating much environmental problems.

ENERGY FROM THE SUN:

Solar energy is the energy coming from the Sun and is used directly and indirectly. Sunlight does not pollute the environment in any way. The sunrays are the ultimate source of life on the Earth. We are dependent on the Sun for all our food and fuels. If we find a suitable method to use a fraction of the solar energy reaching the Earth, then it would be enough to fulfil our energy requirement.

SOLAR HOUSE HEATING:

The use of solar energy is not new. However, it’s use in houses and offices as well as for commercial industrial purposes is quite recent. Complete solar house heating systems are successfully used in areas with a minimum amount of sunshine in winter. A heating system consists of:

A collector
A storage device
A distribution system

Figure shows a solar collector made of glass panels over blank metal plates. The plates absorb the Sun’s energy which heats a liquid flowing in the pipes at the back of the collector. The hot water can be used for cooking, washing and heating the buildings. Solar energy is used in solar cookers, solar distillation plants, solar power plant, etc.

SOLAR CELLS:

Solar energy can also be converted directly into electricity by solar cells. A solar cell also called photocell is made from silicon wafer. When sunlight falls on a solar cell, it converts the light directly into electrical energy.

Solar cells are used in calculators, watches and toys. Large numbers of solar cells are wired together to form solar panels. Solar panels can provide power to telephone booths, light houses and scientific research centres. Solar panels are also used to power satellites.

WIND ENERGY:

Wind has been used as a source of energy for centuries. It has powered sailing ships across the oceans. It has been used by windmills to grind grain and pump water. More recently, wind power is used to turn wind turbines (Figure 6.24). When many wind machines are grouped together on wind farms, they can generate enough power to operate a power plant.

GEOTHERMAL ENERGY:

In some parts of the world, the Earth provides us hot water from geysers and hot springs. There is hot molten part, deep in the Earth called magma. Water reaching close to the magma changes to steam due to the high temperature of magma. This energy is called geothermal energy.

ENERGY FROM BIOMASS:

Biomass is plant or animal wastes that can be burnt as fuel. Other forms of biomass are garbage, farm wastes, sugarcane and other plants. These wastes are used to run power plants.

When animal dung, dead plants and dead animals decompose, they give off a mixture of methane and carbon dioxide. Electricity can be generated by burning methane.

Q What is mass – energy equation?

Einstein predicted the interconversion of matter and energy. According to him, a loss in the mass of a body provides a lot of energy. This happens in nuclear reactions. The relation between mass m and energy E is given by Einstein’s mass-energy equation.

Here c is the speed of light (3×10⁸ ms^-1). The above equation shows that tremendous amount of energy can be obtained from small quantity of matter.

Q How electricity is generated from fossil fuels?

Fossil fuels are burnt in thermal power stationsto produce electricity. Various energy conversion processes involved in producing electricity from coal are described in a block diagram:

Q What are effects of producing energy on environment?

Environmental problems such as pollution that consist of noise, air pollution and water pollution may arise by using different sources of energy such as fossil fuels and nuclear energy. A temperature rise in the environment that disturbs life is called thermal pollution. Thermal pollution upsets the balance of life and endangers the survival of many species.

The burning of fuel and solid wastes in homes, automobiles and factories releases harmful amount of air pollutants.

All power plants produce waste heat, but fission plants produce the most. The heat released into a lake, a river or an ocean upsets the balance of life in them. Unlike other power plants, nuclear power plants do not produce carbon dioxide. But they do produce dangerous radioactive wastes.

Q Name some steps which would reduce the pollution?

Some steps which are helpful to reduce pollution are:

Use of catalytic converter.
Use of lead free petrol.
By using public transport.

Q Draw a flow diagram of an energy converter of:

Electric Lamp:

Energy Saver Lamp:

Vehicle Running with Constant Speed on a Level Road:

Power Station:

Q What is efficiency of a system?

Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input.

Q What is an ideal system?

An ideal system is that which gives an output equal to the total energy used by it. In other words, its efficiency is 100 %. People have tried to design a working system that would be 100 % efficient.

Q Why practically does not exist?

Practically ideal system does not exist. Every system meets energy losses due to friction that causes heat, noise etc. These are not the useful forms of energy and go waste. This means we cannot utilize all the energy given to a working system. The energy in the required form obtained from a working system is always less than the energy given to it as input.

Q What is meant by the term power? Also explain its unit.

Power:

Power is defined as the rate of doing work.

Mathematically:

Since work is a scalar quantity, therefore, power is also a scalar quantity.

Unit:

SI unit of power is watt (W). It is defined as

The power of a body is one watt if it does work at the rate of 1 joule per second (1 Js^-1).

Bigger units of power are kilowatt (kW), megawatt (MW) etc.

1kW = 1000 W = 10³ W

1MW = 1000 000 W = 10⁶ W

1 hours power = 1 hp = 746 W

Exercise

6.1 Encircle the correct answer from the given choices.

c	c	c	d	a	c
b	c	b	b	c

6.2 Define work. What is its SI unit?

Work:

Work is done when a force acting on a body displaces it in the direction of a force.

Mathematically:

Quantity:

Work is a scalar quantity.

Dependence:

It depends on the force acting on a body, displacement of the body and the angle between them.

Unit:

SI unit of work is joule (J). It is defined as

The amount of work is one joule when a force of one newton displaces a body through one metre in the direction of force.

Thus, 1J = 1 N x 1m

Joule is a small unit of work. Its bigger units are:

1 kilo joule (1kJ) = 1000 J = 10³ J

1mega joule (1MJ) =1000 000 J =10⁶J

6.3 When does a force do work? Explain

Work is said to be done when a force acts on a body and moves it in the direction of the force.

6.4 Why do we need energy?

The energy is an important and fundamental concept in science. It links almost all the natural phenomena. When we say that a body has energy, we mean that it has the ability to do work. Water running down the stream has the ability to do work, so it possesses energy. The energy of running water can be used to run water mills or water turbines.

6.5 Define energy, give two types of mechanical energy.

MECHANICAL ENERGY:

Types:

There are two types of mechanical energy.

Kinetic energy
Potential energy

6.6 Define K.E. and derive its relation.

Kinetic Energy:

The energy possessed by a body due to its motion is called its kinetic energy.

Examples:

Moving water in a river.
Wind derives windmills.

Mathematically:

Consider a body of mass m moving with velocity v. The body stops after moving through some distance S due to some opposing force such as force of friction acting on it. The body possesses kinetic energy and is capable to do work against opposing force F until all of its kinetic energy is used up.

……….i

Since motion is opposed, hence, a is negative. Using 3rd equation of motion:

……….ii

From Eq. i and ii we get

6.7 Define potential energy and derive its relation.

Potential Energy:

The energy possessed by a body due to its motion is called its kinetic energy.

Examples:

Stretched bow
Hammer raised up

Mathematically:

Let a body of mass m be raised up through height h from the ground. The body will acquire potential energy equal to the work done in lifting it to height h.

Thus,

6.8 Why fossils fuels are called non-renewable form of energy?

6.9 Which form of energy is most preferred and why?

6.10 How is energy converted from one form to another? Explain.

Energy cannot be destroyed however it can be converted into some other forms.

Processes in nature are the results of energy changes. For example, some of the heat energy from the Sun is taken up by water to evaporate.

6.11 Name the five devices that convert electrical energy into mechanical energy.

Devices that convert electrical energy into mechanical energy.

Electric motor
Drill machine
Electric fan
Electric spinner
Electric grinder

6.12 Name a device that converts mechanical energy into electrical energy.

Electric generator converts mechanical energy into electrical energy.

6.13 What is meant by the efficiency of a system?

Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input.

6.14 How can you find the efficiency of a system?

Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input.

6.15 What is meant by the term power?

Power:

Power is defined as the rate of doing work.

Mathematically:

Since work is a scalar quantity, therefore, power is also a scalar quantity.

Unit:

SI unit of power is watt (W).

6.16 Define watt.

The power of a body is one watt if it does work at the rate of 1 joule per second (1 Js^-1).

Bigger units of power are kilowatt (kW), megawatt (MW) etc.

1kW = 1000 W = 10³ W

1MW = 1000 000 W = 10⁶ W

1 hours power = 1 hp = 746 W

Unit 7

Q State the postulates of the kinetic molecular model of matter.

The kinetic molecular model of matter has some important features. These are:

Matter is made up of particles called molecules.
The molecules are always in continuous motion.
Molecules attract each other.

Q How kinetic molecular model of matter is used to explain three states of matter?

Kinetic molecular model is used to explain the three states of matter – solid, liquid and gas.

SOLIDS:

Solids such as a stone, metal spoon, pencil, etc. have fixed shapes and volume. Their molecules are held close together such as shown in figure by strong forces of attraction. However, they vibrate about their mean positions but do not move from place to place.

LIQUIDS:

The distances between the molecules of a liquid are more than in solids. Thus, attractive forces between them are weaker. Like solids, molecules of a liquid also vibrate about their mean position but are not rigidly held with each other. Due to the weaker attractive forces, they can slide over one another. Thus, the liquids can flow. The volume of a certain amount of liquid remains the same but because it can flow hence, it attains the shape of a container to which it is put.

GASES:

Gases such as air have no fixed shape or volume. They can be filled in any container of any shape.Their molecules have random motion and move with very high velocities. In gases, molecules are much farther apart than solids or liquids such as shown in figure. Thus, gases are much lighter than solids and liquids. They can be squeezed into smaller volumes. The molecules of a gas are constantly striking the walls of a container. Thus, a gas exerts pressure on the walls of the container.

Q What is plasma state of matter?

The kinetic energy of gas molecules goes on increasing if a gas is heated continuously. This causes the gas molecules to move faster and faster. The collisions between atoms and molecules of the gas become so strong that they tear off the atoms. Atoms lose their electrons and become positive ions. This ionic state of matter is called plasma. Plasma is also formed in gas discharge tubes when electric current passes through these tubes. Plasma is called the fourth state of matter in which a gas occurs in its ionic state.

Q What is density?

Density:

Density of a substance is defined as its mass per unit volume.

Mathematically:

Unit:

SI unit of density is kilogramme per cubic metre (kgm^-3).

Density Equations:

Q How density decreases with altitude?

Earth’s atmosphere extends upward about a few hundred kilometres with continuously decreasing density. Nearly half of its mass is between sea level and 10 km. Up to 30 km from sea level contains about 99% of the mass of the atmosphere. The air becomes thinner and thinner as we go up.

Q When we press a pencil from its ends between the palms why the palm pressing the tip feels much more pain than the palm pressing its blunt end?

The effectiveness of a force is increased if the effective area of the force is reduced. The area of the tip of pencil is very small and hence increases the effectiveness of the force.

Q How drawing pin is easily pressed into a drawing board?

Drawing pin is easily pressed into a drawing board because the force we apply on the drawing pin is confined just at a very small area under its sharp tip. A drawing pin with a blunt tip would be very difficult to push into the board due to the large area of its tip. The effectiveness of a small force is increased if the effective area of the force is reduced. The area of the nail is very small and hence increases the effectiveness of the force.

Q Why the soap bubbles so formed have spherical shapes?

The soap bubbles so formed have spherical shapes because the atmospheric pressure acts on a bubble equally in all direction.

Q What is a barometer? Write its construction and explain that how atmospheric pressure is measured using a barometer?

Barometer:

The instrument that measures atmospheric pressure is called barometer.

Types:

On the basis of material barometers are classified into two types.

Mercury Barometer
Water Barometer

Mercury Barometer:

One of the simple barometers is a mercury barometer in which mercury is used as a fill material.

Construction:

It consists of glass tube 1 m long closed at one end. After filling it with mercury it is inverted in mercury through.

Working:

Mercury in the tube descends and stops at a certain height. The column of mercury held in the tube exerts pressure at its base. At sea level the height of mercury column above the mercury in the trough if found to be about 76cm.

Pressure exerted by 76 cm of mercury column is nearly 101,300 Nm^–2 equal to atmospheric pressure. It is common to express atmospheric pressure. It is common to express atmospheric pressure in terms of the height of mercury column. As the atmospheric pressure at a place does not remain constant, hence, the height of mercury column also varies with atmospheric pressure.

Water Barometer:

Another cheap barometer is a water barometer in which water is used as a fill material.

Explanation:

Mercury is 13.6 times denser than water. Atmospheric pressure can hold vertical column at a place. Thus, at sea level, vertical height of water column would be 0.76m × 130.6 = 10.34m. Thus a glass tube more than 10 m long is required to make a water barometer.

Comparison:

By the above calculation it is clear that 11 meter should be the approximate length of glass tube to construct a water barometer. Whereas only 1 meter long glass tube is required to construct the mercury barometer. Hence, water is not suitable material to be used in a barometer.

Q What do you know about vacuum cleaner?

The fan in a vacuum cleaner lowers air pressure in its bucket. The atmospheric air rushes into it carrying dust and dirt with it through its intake port. The dust and dirt particles are blocked by the filter while air escapes out.

Q How does the atmospheric pressure vary with height?

The atmospheric pressure decreases as we go up. The atmospheric pressure on mountains is lower than at sea level. At a height of about 30 km, the atmospheric pressure becomes only 7 mm of mercury which is approximately 1000 Pa. It would become zero at an altitude where there is no air. Thus, we can determine the altitude of a place by knowing the atmospheric pressure at that place.

Q How air is sucked through straw?

When air is sucked through straw with its other end dipped in a liquid, the air pressure in the straw decreases. This causes the atmospheric pressure to push the liquid up the straw.

Q Derive an expression for liquid pressure.

Pressure in liquids:

Liquids exert pressure. The pressure of a liquid acts in all directions. If we take a pressure sensor (a device that measure pressure) inside a liquid, then the, pressure of the liquid varies with the depth of sensor.

Formula:

Derivation:

Consider a surface of area “A” in a liquid at a depth “h” as show by shaded region in figure. The length of the cylinder of liquid over this surface will be the weight “w” of the liquid above this surface “p” is the density of the liquid and “m” is mass of liquid above the surface. As we know that;

As,

Put value of m,

Dependence:

The above expression shows that liquid pressure depends on three factors:

Density of liquid (ρ)
Depth of liquid (h)
Gravitational acceleration (g)

Q How does liquid enters into the syringe?

The piston of the syringe is pulled out. This lowers the pressure in the cylinder. The liquid from the bottle enters into the piston through the needle.

Q State Pascal’s law? Also write its applications.

Pascal’s law:

Pressure, applied at any point of a liquid enclosed in a container, is transmitted without loss to all other parts of the liquid.

An external force applied on the surface of a liquid increases the liquid pressure at the surface of the liquid. This increase in liquid pressure is transmitted equally in all directions and to the walls of the container in which it is filled.

Applications:

Pascal’s law finds numerous applications in our daily life such as automobiles, hydraulic brake system, hydraulic jack, hydraulic press and other hydraulic machine.

Q What do you know about braking systems in vehicles?

The braking systems of cars, buses, etc. also work on Pascal’s law. The hydraulic brakes as shown in figure allow equal pressure to be transmitted throughout the liquid. When brake pedal is pushed, it exerts a force on the master cylinder, which increases the liquid pressure in it. The liquid pressure is transmitted equally through the liquid in the metal pipes to all the pistons of other cylinders. Due to the increase in liquid pressure, the pistons in the cylinders move outward pressing the brake pads with the brake drums. The force of friction between the brake pads and the brake drums stops the wheels.

Q State Archimedes principle. Also derive its mathematical relation.

Statement:

When an object is totally or partially immersed in a liquid, an upthrust acts on it equal to the weight of the liquid it displaces.

Derivation:

Consider a solid cylinder of cross-sectional area A and height h immersed in a liquid as shown in figure. Let h₁ and h₂ be the depths of the top and bottom faces of the cylinder respectively from the surface of the liquid.

If P₁ and P₂ are the liquid pressures at depths h₁ and h₂respectively and p is its density, then according to equation:

Let the force F₁ is exerted at the cylinder top by the liquid due to pressure P₁ and the force F₂ is exerted at the bottom of the cylinder by the liquid due to P₂.

F₁and F₂ are acting on the opposite faces of the cylinder. Therefore, the net force F will be F₂ – F₁ in the direction of F₂. This net force F on the cylinder is called the upthrust of the liquid.

Above equation shows that an upthrust acting on the body immersed in a liquid is equal to the weight of liquid displaced.

Q What is hydrometer?

Hydrometer is a glass tube with a scale marked on its stem and heavy weight in the bottom. It is partially immersed in a fluid, the density of which is to be measured. One type of hydrometer is used to measure the concentration of acid in a battery. It is called acid meter.

Q How can we find density of an object?

Archimedes principle is also helpful to determine the density of an object. The ratio in the weights of a body with an equal volume of liquid is the same as in their densities.

= D

According to Archimedes principle, is less than its actual weight by an amount w.

Thus, finding the weight of the solid in air w₁ and its weight in water w₂ , we can calculate the density of the solid by using equation.

Q Describe principle of floatation.

Statement:

A floating object displaces a fluid having weight equal to the weight of the object.

Explanation:

An object sinks if its weight is greater than the upthrust acting on it. An object floats if its weight is equal or less than the upthrust. When an object floats in a fluid, the upthrust acting on it is equal to the weight of the object. In case of floating object, the object may be partially immersed. The upthrust is always equal to the weight of the fluid displaced by the object. Archimedes principle is applicable on liquids as well as gases.

Q How wooden block floats on water?

A wooden block floats on water. It is because the weight of an equal volume of water is greater than the weight of the block. According to the principle of floatation, a body floats if it displaces water equal to the weight of the body when it is partially or completely immersed in water.

Q How ships and boats floats on water?

Ships and boats are designed on the principle of floatation. They floats because the weight of an equal volume of water is greater than the weight of the ships and boats. According to the principle of floatation, a body floats if it displaces water equal to the weight of the body when it is partially or completely immersed in water.

Q What is meant by a deforming force?

Deforming Force:

The applied force that changes shape, length or volume of substance is called deforming force. In most of the cases, the body returns to its original size and shape as soon as the deforming force is removed.

Q Define elasticity.

The property of a body to restore its original size and shape as the deforming force ceases to act is called elasticity.

Q What is stress?

Stress is related to the force producing deformation. It is defined as

The force acting on unit area at the surface of a body is called stress.

Mathematically:

Stress =

Unit:

SI unit of stress is Nm^-2

Q What is tensile strain? Why I has no unit?

When stress acts on a body, it may change its length, volume, or shape. A ratio of such a change caused by the stress with the original length, volume or shape is called as strain. If stress produces a change in the length of an object then the strain is called tensile strain.

It has not unit because it is a ratio between two similar quantities.

Q State Hooke’s law. What is elastic limit and what happen when elastic limit is crossed?

Statement:

The strain produced in a body by the stress applied to it is directly proportional to the stress within the elastic limit of the body.

Mathematically:

Hooke’s law is applicable to all kinds of deformation and all types of matter i.e., solids, liquids or gases within certain limit.

Elastic Limit:

The limit, within which a body recovers its original length, volume or shape after removing deforming force, is called elastic limit.

When a stress crosses elastic limit, a body is permanently deformed and is unable to restore its original state after the stress is removed.

Q Define young’s modulus. Also derive its mathematical formula.

Young’s Modulus:

Definition:

The ratio of stress to tensile strain called Young’s modulus.

Formula:

Its formula is

Units:

Its SI Unit is newton per square (Nm^–2)

Explanation:

Consider a long bar of length L_O and cross sectional area A. Let an external force F equal to the weight w stretched it such that the stretched length becomes L. According to Hooke’s Law, the ratio of this stress to tensile strain is constant within the elastic limit of the body.

Derivation:

Let ∆L be the change in length of the rod, then

As we know that

And,

Putting the values of stress and tensile strain

Dependence:

Young’s modulus only depends upon nature of material.

Exercise

7.1 Encircle the correct answer from the given choices.

a	c	b	d	d
c	b	c	d	a

7.2 How kinetic molecular model of matter is helpful in differentiating various states of matter?

States of matter depends on motion and attraction of molecules. Kinetic molecular model explain the motion and attraction of molecules. Kinetic molecular model states that:

Matter is made up of particles called molecules.
The molecules are always in continuous motion.
Molecules attract each other.

7.3 Does there exist a fourth state of matter? What is that?

Yes, there exist a fourth state of matter. The kinetic energy of gas molecules goes on increasing if a gas is heated continuously. This causes the gas molecules to move faster and faster. The collisions between atoms and molecules of the gas become so strong that they tear off the atoms. Atoms lose their electrons and become positive ions. This ionic state of matter is called plasma.

7.4 What is meant by density? What is its SI unit?

Density:

Density of a substance is defined as its mass per unit volume.

Mathematically:

Unit:

SI unit of density is kilogramme per cubic metre (kgm^-3).

7.5 Can we use a hydrometer to measure the density of milk?

Hydrometer is a device used to measure density of any liquid. So, we can use a hydrometer to measure the density of milk.

7.6 Define the term pressure.

The force acting normally per unit area on the surface of a body is called pressure.

Pressure is a scalar quantity. In SI units, the unit of pressure is Nm^-2 also called pascal (Pa). Thus 1 Nm^-2 = 1Pa

7.7 Show that atmosphere exerts pressure.

The Earth is surrounded by a cover of air called atmosphere. It extends to a few hundred kilometres above sea level. Just as certain sea creatures live at the bottom of ocean, we live at the bottom of a huge ocean of air. Air is a mixture of gases. Due to the force of gravity these gases experience pressure. Anything inside the atmosphere also experience pressure which is known as atmospheric pressure.

7.8 It is easy to remove air from a balloon but it is very difficult to remove air from a glass bottle. Why?

This is because the air inside the balloon is at a fairly high pressure than the atmosphere pressure air outside the balloon. On the other hand air pressure

inside the glass bottle is already equal to the atmospheric pressure so it is difficult to remove air from a glass bottle.

7.9 What is a barometer?

The instruments that measure atmospheric pressure are called barometers. One of the simple barometers is a mercury barometer. It consists of a glass tube 1 metre long closed at one end.

7.10 Why water is not suitable to be used in a barometer?

Mercury is 13.6 times denser than water.Atmospheric pressure can hold vertical column of water about 13.6 times the height of mercury column at a place. Thus, at sea level, vertical height of water column would be 0.76 m x 13.6 = 10.34 m. Thus, a glass tube more than 10 m long is required to make a waterbarometer.

7.11 What makes a sucker pressed on a smooth wall sticks to it?

When a sucker pressed on a smooth wall, the air pressure inside it becomes very small as compared to the air pressure above it. So, it sticks with the smooth surface.

7.12 Why does the atmospheric pressure vary with height?

7.13 What does it mean when the atmospheric pressure at place fall suddenly?

A gradual and average drop in atmospheric pressure means a low pressure in a neighbouring locality.
Minor but rapid fall in atmospheric pressure indicates a windy and showery condition in the nearby region.
A decrease in atmospheric pressure is accompanied by breeze and rain.
A sudden fall in atmospheric pressure often followed by a storm, rain and typhoon to occur in few hours’ time.

7.14 What changes are expected in weather if the barometer reading shows a sudden increase?

An increasing atmospheric pressure with a decline later on predicts an intense weather conditions.
A gradual large increase in the atmospheric pressure indicates a long spell of pleasant weather.
A rapid increase in atmospheric pressure means that it will soon be followed by a decrease in the atmospheric pressure indicating poor weather ahead.

7.15 State Pascal’s law.

Pressure, applied at any point of a liquid enclosed in a container, is transmitted without loss to all other parts of the liquid.

7.16 Explain the working of hydraulic press.

Hydraulic press is a machine which works on Pascal’s law. It consists of two cylinders of different cross-sectional areasas shown in figure. They are fitted with pistons of cross-sectional areas a and A. The object to be compressed is placed over the piston of large cross-sectional area A. The force F₁ is applied on the piston of small cross-sectional area a. The pressure P produced by small piston is transmitted equally to the large piston and a force F₂ acts on A which is much larger than F₁.

Pressure on piston of small area a is given by:

Apply Pascal’s law, the pressure on large piston of area A will be the same as on small piston.

Comparing the above equations, we get

Conclusion:

Since the ratio is greater than 1. Hence, the force F₂ that acts on the larger piston is greater than the force F₁ acting on the smaller piston. Hydraulic systems working in this way are known as force multipliers.

7.17 What is meant by elasticity?

The property of a body to restore its original size and shape as the deforming force ceases to act is called elasticity.

7.18 State Archimedes principle.

When an object is totally or partially immersed in a liquid, an upthrust acts on it equal to the weight of the liquid it displaces.

7.19 What is upthrust? Explain the principle of floatation.

Upthrust:

The force that pushes an object immersed in a liquid in the upward direction is known as up thrust.

Principle of Floatation:

A floating object displaces a fluid having weight equal to the weight of the object.

7.20 Explain how a submarine moves up the water surface and down into water.

A submarine can travel over as well as under water. It works on the principle of floatation. It floats over water when the weight of water equal to its volume isgreater than its weight. Under this condition, it is similar to a ship and remains partially above water level. It has a system of tanks which can be filled with and emptied from seawater. When these tanks are filled with seawater, the weight of the submarine increases. As soon as its weight becomes greater than the upthrust, it dives into water and remains under water. To come up on the surface, thetanks are emptied from seawater.

7.21 Why does a piece of stone sink in water but a ship with a huge weight floats?

According to principle of floatation, a body floats if it displaces water to the weight of the body when it is partially or completely immersed in water.The weight of stone is greater than upthrust that’s why stone sink in water but ship with huge weight floats because it works on the principle of floatation. The weight of ship is less than upthrust that’s why ship floats on a water.

7.22 What is Hooke’s law? What is meant by elastic limit?

Statement:

The strain produced in a body by the stress applied to it is directly proportional to the stress within the elastic limit of the body.

Mathematically:

Hooke’s law is applicable to all kinds of deformation and all types of matter i.e., solids, liquids or gases within certain limit.

Elastic Limit:

The limit, within which a body recovers its original length, volume or shape after removing deforming force, is called elastic limit.

When a stress crosses elastic limit, a body is permanently deformed and is unable to restore its original state after the stress is removed.

7.23 Take a rubber band. Construct a balance of your own using a rubberband. Check its accuracy by weighing various objects.

We know that the length of a rubber band increases on stretching it. Similarly, the pointer of a spring balance is lowered when a body is suspended from it. It is because the length of the spring inside the balance increases depending upon the weight of the suspended body.A rubber band scale will be fairly accurate but only for a short tune. Eventually the rubber band will begin to stretch and wear out. A better scale may be made by substituting a metal spring for the rubber band. Such a scale will be just as accurate, and because the spring is made of metal, it will last much longer.

Unit 8

Q What do you know about thermal equilibrium?

If two objects at different temperatures are joined together, after a certain time they attain the same temperature. This state is called a thermal equilibrium.

Q When you place a cup of hot tea or water in a room, it cools down gradually. Does it continue cooling?

It stops cooling as it reaches the room temperature. Heat flows from a hot body to a cold body until thermal equilibrium is reached.

Q What happens when we touch a hot body?

As, heat flows from a hot body to a cold body until thermal equilibrium is reached.When we touch a hot body heat flows from hot body to our body and we fell hot.

Q On what factors internal energy of a body depends?

Internal energy of a body depends on many factors such as the mass of the body, kinetic and potential energies of molecules etc. Kinetic energy of an atom or molecule is due to its motion which depends upon the temperature. Potential energy of atoms or molecules is the stored energy due to intermolecular forces.

Q What is thermometer? Write properties of thermometric liquid.

Thermometer:

A device that is used to measure the temperature of a body is called thermometer.

Properties:

A thermometric liquid should have the following properties:

It should be visible.
It should have uniform thermal expansion.
It should have a low freezing point.
It should have a high boiling point.
It should not wet glass.
It should be a good conductor of heat.
It should have a small specific heat capacity.

Q What is liquid-in-glass thermometer?

A liquid-in-glass thermometer has a bulb with a long capillary tube of uniform and fine bore such as shown in figure. A suitable liquid is filled in the bulb. When the bulb contacts a hot object, the liquid in it expands and rises in the tube. The glass stem of a thermometer is thick and acts as a cylindrical lens. This makes it easy to see the liquid level in the glass tube.

Q What are lower and upper fixed points in a thermometer?

A thermometer has a scale on its stem. This scale has two fixed points. The lower fixed point is marked to show the position of liquid in the thermometer when it is placed in ice. Similarly, upper fixed point is marked to show the position of liquid in the thermometer when it is placed in steam at standard pressure above boiling water.

Q Explain scales of temperature.

A scale is marked on the thermometer. The temperature of the body in contact with the thermometer can be read on that scale. Three scales of temperature are in common use.

Celsius scale or centigrade scale
Fahrenheit scale
Kelvin scale

Conversion of Temperature:

From Celsius to Kelvin Scale:

T(K) = 273 + C

From Kelvin to Celsius scale:

C = T (K) – 273

From Celsius to Fahrenheit Scale:

F = 1.8 C + 32

From Fahrenheit to Celsius Scale:

Q Which of the following substances have greater average kinetic energy of its molecules at 10^oC?

(a) steel (b) copper

(c) water (d) mercury

Copper have greater average kinetic energy of its molecules at 10^oC

Q Every thermometer makes use of some property of a material that varies with temperature. Name the property used in:

(a) strip thermometers

In strip thermometers colour variation is used.

(b) mercury thermometers

In mercury thermometers uniform thermal expansion is used.

Q What is clinical thermometer?

A clinical thermometer is used to measure the temperature of human body. It has a narrow range from 35 °C to 42 °C. It has a constriction that prevents the mercury to return. Thus, its reading does not change until reset.

Q Why water is used as a coolant in the radiator or automobiles?

Water has a large specific heat capacity. For this reason, it is very useful in storing and carrying thermal energy due to its high specific heat capacity. The cooling system of automobiles uses water to carry away unwanted thermal energy. In an automobile, large amount of heat is produced by its engine due to which its temperature goes on increasing. The engine would case unless it is not cooled down. Water circulating around the engine maintains its temperature. Water absorbs unwanted thermal energy of the engine and dissipates heat through its radiator.

Q Define heat capacity.

Heat capacity of a body is the quantity of thermal energy absorbed by it for one kelvin (1 K) increase in its temperature.

Q How cooling is produced in refrigerators?

Cooling is produced in refrigerators by evaporation of liquid gas. This produces cooling effect. Freon, a CFC was used as a refrigerant gas. But its use has been forbidden when it was known that CFC is the cause of ozone depletion in the upper atmosphere which results increase in amount of UV rays from the Sun. The rays are harmful to all living matter. Freon gas is now replaced by ammonia and other substances which are not harmful to the environment.

Q Why evaporation cause cooling?

During evaporation fast moving molecules escape out from the surface of the liquid. Molecules that have lower kinetic energy are left behind. This lowers the average kinetic energy of the liquid molecules and temperature of the liquid. Since temperature of a substance depends on the average kinetic energy of its molecules.

Q Why wet clothes dry up rapidly when spread?

As, evaporation is the changing of a liquid into vapours (gaseous state) from the surface of the liquid without heating it. Evaporation take place from the surface so we spread cloths to increase their surface area.

Q How specific heat differs from heat capacity?

Specific heat	Heat capacity
Specific heat of a substance is the amount of heat required to raise the temperature of one kg mass of that substance through 1k.	Heat capacity of a body is the quantity of thermal energy absorbed by it for one kelvin (1 K) increase in its temperature.
Its SI Unit Jkg^–1 k^–1	Its unit is JK^-1

Q Give two uses of cooling effect by evaporation.

It helps to moderate the temperature of our climate.
It lowers the temperature of our body.

Q How evaporation differs from vaporization?

Evaporation	Vaporization
Evaporation is the changing of a liquid into vapours (gaseous state) from the surface of the liquid without heating it.	The process in which liquid converts into gas at its boiling point is called vaporization.
It takes place at all temperatures.	It take place at boiling point.
In this process liquid change into vapours from the surface of liquid.	In this process liquid change into vapours not only from surface but also within the liquid.

Q Define thermal expansion. Why does a substance expand on heating?

Thermal Expansion:

Most of the substances i.e. solids, liquids and gases expand on heating. This phenomenon is called thermal expansion.

Reason:

The kinetic energy of the molecules of on object depends on its temperature. The molecules of solid vibrate with larger amplitude at high temperature than at low temperature. Thus, on heating the amplitude of vibration of the atoms molecules of an object increases. They push one another farther away as the amplitude of vibration increases.

Q Define linear thermal expansion in solids. Derive a mathematical relation for linear thermal expansion.

Linear Thermal Expansion:

Definition:

The length of a solid changes with the change in temperature and is called linear thermal expression.

Derivation:

Before expansion of a solid initial length was “L_o” at certain temperature “T_o”. On heating the solid to a temperature T, its length became “L”. Thus,

Change in length ΔL = L – L_o

Change in temperature ΔT = T – T_o

The change in length AL is proportional to its original length L_o and change in temperature ΔT. Thus,

ΔL L_oΔT

ΔL = α L_oΔT

L – L_o = α L_oΔT

L = L_o + α L_oΔT

L = L_o (1+ α ΔT)

Where α is called the coefficient of linear thermal expansion.

Coefficient of linear expansion:

Definition:

The fractional change in length of a substance per Kelvin change in temperature is called coefficient of linear thermal expansion.

Formula:

Its formula is

Unit:

Its SI unit is per Kelvin (K^–1)

Q Why the coefficient of volume expansion of liquids is greater than solids?

The molecules of liquids are free to move in all directions within the liquid. On heating a liquid, the average amplitude of Vibration of its molecules increases. The molecules push each other and need more space to occupy. This accounts for the expansion of the liquid when heated. The thermal expansion in liquids is greater than solids due to the weak forces between their molecules. Therefore, the coefficient of volume expansion of liquids is greater than solids.

Q Why gaps are left in railway tracks?

The expansion of solids may damage the railway tracks as they are constantly subjected to temperature changes. So provision is made during construction for expansion and contraction with temperature. Railway tracks buckled on a hot summer day due to expansion if gaps are not left between sections.

Q Why gaps are left in bridges with rollers?

The expansion of solids may damage the bridges as they are constantly subjected to temperature changes. Bridges made of steel girders expand during the day and contract during night. They will bend if their ends are fixed. To allow thermal expansion, one end is fixed while the other end of the girder rests on rollers in the gap left for expansion.

Q Why overhead transmission lines (wires on electric poles) are given a certain amount of sag?

Overhead transmission lines are also given a certain amount of sag so that they can contract in winter without snapping.

Q List the application of thermal expansion?

In thermometers, thermal expansion is used in temperaturemeasurements.
To open the cap of a bottle that is tight enough, immerse it in hot water for a minute or so. Metal cap expands and becomes loose. It would now be easy to turn it to open.
To join steel plates tightly together, red hot rivets are forced through holes in the plates. The end of hot rivet is then hammered. On cooling, the rivets contract and bring the plates tightly gripped.
Iron rims are fixed on wooden wheels of carts. Iron rims are heated. Thermal expansion allows them to slip over the wooden wheel. Water is poured on it to cool. The rim contracts and becomes tight over the wheel.

Q What are bi metal strips? Write down there uses.

A bimetal strip consists of two thin strips of different metals such as brass and iron joined together. On heating the strip, brass expands more than iron. This unequal expansion causes bending of the strip.

Uses:

Bimetal strips are used for various purposes. Bimetal thermometers are used to measure temperatures especially in furnaces and ovens. Bimetal strips are also used in thermostats. Bimetal thermostat switch is used to control the temperature of heater coil in an electric iron.

Q What is anomalous expansion of water?

Water on cooling below 4°C begins to expand until it reaches 0°C. On further cooling its volume increases suddenly as it changes into ice at 0°C. When ice is cooled below 0°C, it contracts i.e. its volume decreases like solids. This unusual expansion of water is called the anomalous expansion of water.

Q What is meant by real and apparent expansion of liquid?

Real Expansion:

The expansion of the volume of liquid taking into consideration the expansion of the container also, is called the real volume expansion of the liquid.

Apparent Expansion:

The expansion of the volume of a liquid without into consideration the expansion of the container also, it called the apparent volume expansion of the liquid.

Q What is the importance of large specific heat capacity of water?

Large specific heat capacity of water is important in many ways.

Storing and carrying thermal energy.
Cooling system of auto mobiles use water to carry away unwanted thermal energy.
Central heating system.
Helps to moderate climate.

Exercise

8.1 Encircle the correct answer from the given choices.

b	b	d	c
a	b	b	d

8.2 Why does heat flow from hot body to cold body?

Heat flows from hot body to cold body due to temperature difference. Hot body radiate heat while cold body absorbs heat until both the bodies come in thermal equilibrium.

8.3 Define the terms heat and temperature.

Temperature:

Temperature of a body is the degree of hotness or coldness of the body.

Heat:

Heat is the energy that is transferred from one body to the other in thermal contact with each other as a result of the difference of temperature between them.

8.4 What is meant by internal energy of a body?

The sum of kinetic energy and potential energy associated with the atoms, molecules and particles of a body is called its internal energy.

8.5 How does heating affect the motion of molecules of a gas?

When gas is heated, the kinetic energy of gas molecules increases. So molecules collide with each other with more energy, which increases the internal energy of gas.

8.6 What is a thermometer? Why mercury is preferred as a thermometric substance?

Thermometer:

A device that is used to measure the temperature of a body is called thermometer.

Properties:

Mercury freezes at-39 °C and boils at 357 °C. It has all the thermometric properties such as:

It should be visible.
It should have uniform thermal expansion.
It should have a low freezing point.
It should have a high boiling point.
It should not wet glass.
It should be a good conductor of heat.
It should have a small specific heat capacity.

8.7 Explain the volumetric thermal expansion.

The volume of a solid also changes with the change in temperature and is called volume thermal expansion or cubical thermal expansion. Consider a solid of initial volume Vo at certain temperature To . On heating the solid to a temperature T, let its volume becomes V, then

Change in volume ΔV = V – V_o

Change in temperature ΔT = T – T_o

Like linear expansion, the change in volume ΔV is found to be proportional to its original volume Vo and change in temperature ΔT. Thus

ΔVV_oΔT

ΔV= βV_oΔT

V – V_o = βV_oΔT

V = V_o + βV_oΔT

V = V_o (1+ β ΔT)

Where β is called the coefficient of volume thermal expansion.

Coefficient of linear expansion:

Definition:

“The temperature coefficient of volume expansion as the fractional change in its volume per kelvin change in temperature.”

Formula:

Its formula is

8.8 Define specific heat. How would you find the specific heat of a solid?

Definition:

Specific heat of a substance is the amount of heat required to raise the temperature of one kg mass of that substance through 1k.

Formula:

Its formula is

Unit:

Its SI Unit is Joule per kg per kelvin(Jkg^–1 k^–1)

Dependence:

The value of specific heat depends upon the nature of material only.

Explanation:

When a body is heated, its temperature increases. Increase in the temperature of a body is found to be proportional to the amount of heat absorbed by it. It has also been observed that the quantity of heat ΔQ required to raise the temperature ΔT of a body is proportional to the mass m of the body. Thus

……..i

……….ii

By combining equation (i) and (ii)

Here ΔQ is the amount of heat absorbed by the body and C is the constant of proportionality called the specific heat capacity or simply specific heat.

Specific Heat of a Solid:

The method of mixture is used to find specific heat of a solid.

8.9 Define and explain latent heat of fusion.

Latent Heat of Fusion:

Heat energy required to change unit mass of a substance from solid to liquid state at its melting point without change in its temperature is called its latent heat of fusion.

Formula:

Its formula is

Unit:

Its unit is joule per kilogram(Jkg^–1)

Fusion point / Melting Point:

The temperature at which a solid starts melting is called its fusion point or melting point.

Freezing Point:

The temperature at which a substance changes from liquid to solid is called its freezing point.

8.10 Define latent heat of vaporization

The quantity of heat that changes unit mass of a liquid completely into gas at its boiling point without any change in its temperature is called its latent heat of vaporization.

It is denoted by

8.11 What is meant by evaporation? On what factors the evaporation of a liquid depends? Explain how cooling is produced by evaporation.

Definition:

Evaporation is the changing of a liquid into vapours (gaseous state) from the surface of the liquid without heating it.

Factors Affecting the Rate of Evaporation of a Liquid:

Evaporation takes place at all temperature from the surface of a liquid. The rate of evaporation is affected by various factors.

Temperature
Surface Area
Wind
Nature of the Liquid

Explanation:

Temperature:

At higher temperature, more molecules of a liquid are moving with high velocities. Thus, more molecules escape from its surface. Thus, evaporation is faster at high temperature than at low temperature.

Surface Area:

Larger is the surface area of a liquid, greater number of molecules has the chance to escape from its surface.

Wind:

Wind blowing over the surface of a liquid sweeps away the liquid molecules that have just escape out. This increases the chance for more liquid molecules to escape out.

Nature of the Liquid:

Evaporation depends on the nature of the liquid. For example when we put few drops of ether or spirit on our palm we feel cool because rate of evaporation is high. Due to evaporation we feel cool.

Evaporation Produce Cooling:

Unit 9

Q What do you mean by transfer of heat?

The flow of heat energy from hot body to cold body when both bodies are in thermal contact with each other is called transfer of heat. Transfer of heat is a natural process. It continues all the time as long as the bodies in thermal contact are at different temperature.

Modes of Transfer of Heat:

There are three ways by which transfer of heat take place. These are

Conduction
Convection
Radiation

Q What happens when one end of solid is heated?

The atoms or molecules present at that end begin to vibrate more rapidly. They also collide with their neighbouring atoms or molecules. In doing so, they pass some of their energy to neighbouring atoms or molecules during collisions with them will increase in their vibrations. These atoms or molecules in tern pass on a part of the energy to their neighbouring particles. In this way some heat reaches the other parts of the solids.

Q Why heat transfer rapidly in metals than non-metals?

Metals have free electrons. These free electrons move with very high velocities within the metal objects. They carry energy at a very fast rate from hot to cold parts of the object as they move. Thus, heat reaches the cold parts of the metals objects from its hard parts much more quickly than non-metals.

Q What is conduction?

The mode of transfer of heat by vibrating atoms and free electrons in solids from hot to cold parts of a body is called conduction of heat.

Q Why Styrofoam boxes are used to keep food hot or ice cream cold for a long time?

Styrofoam boxes are used to keep food hot or ice cream cold for a long timeStyrofoam is a bad conductor of heat. It does not allow heat to leave or enter the box easily.

Q Give two disadvantages of conduction.

Disadvantages of Conduction:

This is a slow process.
Very small transfer of heat takes place from hot to cold parts in solids.

Q Differentiate between conductors and insulators.

Sr.	Conductors	Insulators
1	The substances that allow heat to pass through them are called conductors of heat.	The substances through which the heat does not conduct easily are called bad conductors or insulators.
2	Conductors have free electrons.	Insulators have no free electrons.
3	The value of thermal conductivity of conductor is very high.	The value of thermal conductivity of insulators is very low.
4	Example: aluminium, iron, copper etc.	Example: Wood, cork, cotton, glass, rubber etc.

Q What is meant by rate of flow of heat? On what factors it depends?

Rate of flow of heat:

The amount of heat that flow in unit time is called the rate of flow of heat.

Formula:

Unit:

SI unit of rate of flow of heat is joule per second orJs^–1.

Dependence:

It is observed that the rate at which heat flows through a solid object depends upon various factors.

Cross sectional area of the solid
Length of the solid
Temperature difference between ends

Cross – Sectional area of the solid:

Larger cross sectional Area A of solid contains larger number of molecules and free electrons on each layer parallel to its cross sectional area and hence greater will be the rate of flow of heat through the solid.

A …………… (1)

Length of the solid:

Larger is the length between the hot and cold ends of the solid, more time it will take to conduct heat to the colder end and smaller will be the rate of flow of heat.

…………… (2)

Temperature difference between ends:

Greater is the temperature difference T₁ – T₂ between hot and cold faces of the solids, greater will be rate of low of heat. Thus

…………… (3)

Combining equation (1) (2) and (3)

Here k is the proportionality constant called thermal conductivity of solid.

Q Define the term thermal conductivity. On what factors it depends upon?

Thermal Conductivity:

The rate of flow of heat across the opposite faces of meter Cube of substance maintained at a temperature difference of one Kelvin is called the thermal conductivity of that substance.

Formula:

Unit:

SI unit of thermal conductivity is Wm^–1K^–1.

Dependence:

Thermal conductivity of substances depends upon:

The nature of material.
Temperature difference.
Cross-sectional area.
Length
Time.

Q Write some uses of conductors.

Uses of conductors:

Good conductors are used when quick transfer of heat is required through a body.
Cookers, cooking plates, boiler, radiators and condensers of refrigerators, etc. are made of metals such as aluminium and copper for the better conduction.
Metal boxes are used for making ice, ice cream, etc.
Sauce pans are made of metal for quick heat transfer.

Q Give some uses of insulators / bad conductors.

Uses of Insulators:

Insulators or bad conductors are used in home utensils such as handles of sauce pans, hot plates, spoons etc. they are made up of wood or plastic.
Air is one of the bad conductors or best insulator. That is why cavity walls i.e two walls separated by an air space and double glazed windows keep the houses warm in winter and cool in summer.
Some of the non-conductors are used for laggings to insulate water pipes, hot water cylinders, ovens, refrigerators, walls and roofs of houses.
Woollen cloth is used to make warm winter clothes.
Feathers give good thermal insulation especially when fluffed up.

Q Define convection.

Transfer of heat by actual movement of molecules from hot place to a cold place is known as convection.

Q Write some uses of convection currents.

Uses of Convection Current:

Convection currents set up by electric, gas or coal heaters help to warm our homes and offices.
Central heating systems in buildings work on the same principle air convection.
Convection current occurs on a large scale in nature. The day to day temperature changes in the atmosphere result from the circulation m warm or cold air that travels across the region.
Land and sea breezes are also the examples convection currents.
Air fans also set up convection currents to blow the air in the room. This phenomenon is called forced convection currents.

Q Is Convection occurs in solids?

Convection occurs in liquids and gases only because their molecules can move freely. The molecules of a solid are held closely together. They cannot move freely. The molecules of a solid are held closely together. They cannot move freely, therefore, convection is not possible in solids.

Q Why a balloon inflated with hot rise up?

A liquid or a gas becomes lighter (less dense) as it expands on heating. Hot liquid or gas rises up above the heated area. The cooler liquid or gas from the surrounding fills the places which in turns is heated up.

Q What cause a glider to remain in air?

A glider such as look like a small aero plane without engine. Glider pilots use upward movement of hot air currents due to convection of heat. These rising currents of hot air are called thermals. Glider ride over these thermal. The upward movement of air currents in thermal help them to stay in air for a long period.

Q How do thermals help birds to fly for hours without flapping their wings?

The birds stretch out their wings and circle in these thermals. The upward movement of air helps birds to climb up with it. Eagles, hawks and vultures are expert thermal climbers. After getting the free lift, birds are able to fly for hours without flapping their wings. They glide from one thermal to another and thus travel through large distances and hardly need to flap their wings.

Q What is Gliding Flights of Birds?

The birds stretch out their wings and circle in the rising currents of hot air called thermals. The upward movement of these thermals (air thermals) helps birds to climb up with it. Eagles, hawks and vultures are expert thermal climbers. After getting a free lift (over thermals), birds are able to fly for hours without flapping their wings They glide from one thermal to another and thus travel through large distance and hardly need to flap their wings.

Q Why does see breeze below during the day?

Sea breezes are the result of convection. On a hot day, the temperature of the land increases more quickly than the sea. It is because the specific heat of land is much smaller as compared to water. The air above land gets hot and rises up. Cold air from the sea begins to move towards the land. It is called see breeze.

Q Why does land breeze below in the night?

Land breezes are the result of convection. At night, the land cools faster than the sea. Therefore, air above the sea is warmer, rises up and the cold air from the land begins to move towards the sea. It is called sea breeze.

Q How does heat reach us directly from a fireplace?

Hot air moves upward from the fireplace. Heat from the fireplace reaches us directly in the form of waves called radiation.

Q How does the land and sea breezes help to keep the temperature moderate in coastal areas?

On a hot day, the temperature of the land increases more quickly than the sea. It is because the specific heat of land is much smaller as compared to water. The air above land gets hot and rises up. Cold air from the sea begins to move towards the land. At night, the land cools faster than the sea. Therefore, air above the sea is warmer, rises up and the cold air from the land begins to move towards the sea.

Q Why does a cup of hot tea become cold after sometime?

All the objects are radiating heat. However, they are also absorbing heat at the same time. When temperature of an object is higher than its surroundings then it radiating more heat than it is absorbing. As a result, its temperature goes on decreasing till it becomes equal to its surroundings.

Q Why does a glass of chilled water become hot after sometime?

All the objects are radiating heat. However, they are also absorbing heat at the same time. When temperature of an object is lower than its surroundings then it radiating less heat than it is absorbing. As a result, its temperature goes on increasing till it becomes equal to its surroundings.

Q Define radiation. On what factors the rate of radiation depends upon? Explain all the factors in detail.

Definition:

Radiation is the mode of transfer of heat from one place to another in the form of waves called electromagnetic waves. Factors effecting on radiation

Radiations are emitted by all bodies. The rate at which radiations are emitted from a body depends upon various factors. Some of these are:

Colour and Texture of the surface
Surface Temperature
Surface Area

Explanation:

Colour and Texture of the Surface:

When temperature of an object is lower than its surroundings, then it is radiating less heat than it is absorbing. As a result, its temperature goes on increasing till it becomes equal to its surroundings. The rate at which various surfaces emit heat depends upon the nature of the surface. Various surfaces can be compared using Leslie’s cube.

Emission and Absorption of Radiation:

A Leslie cube is a metal box having faces of different nature as shown in figure. The four faces of Leslie’s cube may be as following:

A shining silvered surface
A dull black surface
A white surface
A coloured surface

Hot water is filled in the Leslie’s cube and is placed with one of its face towards a radiation detector. It is found that black dull surface is good emitter of heat.

The rate at which various surfaces absorb heat also depends upon the nature of those surfaces. For example, take two surfaces, one is dull black and the other is a silver polished surface with a candle at the middle of the surface.

Conclusion:

A dull black surface is a good absorber of heat as its temperature rises rapidly.

A polished surface is poor absorber of heat as its temperature rises very slowly. The observations made from the above experiment are given in the table given below.

Surfaces	Emitter	Absorber	Reflector
Dull black surface	Best	Best	Worst
Coloured surface	Good	Good	Bad
White surface	Bad	Bad	Good
Shining slivered surface	Worst	Worst	Best

Surface Temperature:

When the temperature of an object is higher than its surroundings like hot cup of tea, then it is radiating more heat than it is absorbing. On the other hand, when the temperature of an object is lower than its surrounding like chilled water, then it is radiating less heat than it is absorbing.

Surface Area:

It is also found that the transfer of heat by radiation is also affected by the surface area of the body emitting or absorbing heat. Larger is the area, greater will be the transfer of heat. It is due to this reason that larger numbers of slots are made in radiators to increase their surface area.

Q How temperature is maintain in thermos flask?

In a thermos flask, most of the heat is prevented to enter or leave the flask. This is done by suitable measures to reduce the transfer of heat due to conduction, convection and radiation. Thus, anything kept in it, maintains its temperature for a long time.

Q Why the bottoms of cooking pots are made black?

The amount of heat absorbed by a body depends upon the colour and nature of its surface. A black and rough surface absorbs more heat than a white orpolished surface. Since good absorbers are also good radiators of heat. Thus, a black coloured body gets hot quickly absorbing heat reaching it during a sunny day and also cools down quickly by giving out its heat to its surroundings. The bottoms of cooking pots are made black to increase the absorption of heat from fire.

Q Why we wear white cloths during hot days?

Like light rays, heat radiations also obey laws of reflection. The amount of heat reflected from an object depends upon its colour and nature of the surface. White surfaces reflect more than coloured or black surfaces.Hence, we wear white or light coloured clothes in summer which reflect most of the heat radiation reaching us during the hot day.

Q Why we polish interior of the cooking and hot pots?

Like light rays, heat radiations also obey laws of reflection. The amount of heat reflected from an object depends upon its colour and nature of the surface. White surfaces reflect more than coloured or black surfaces. Hence, we polish the interior of the cooking and hot pots for reflecting back most of the heat radiation within them.

Exercise

9.1 Encircle the correct answer from the given choices.

b	c	a	c	d
d	b	c	b

9.2 Why metals are good conductors of heat?

9.3 Explain why:

(a) a metal feels colder to touch than wood kept in a cold place?

Heat transfer from hot body to cold body. As metal is a good conductor of heat so when we touch metal more heat is transferred and we feel colder. Wood is a non-metal so less heat is transferred and we feel less cold.

(b) land breeze blows from land towards sea?

(c) double walled glass vessel is used in thermos flask?

(d) deserts soon get hot during the day and soon get cold after sunset?

The specific heat of sand is low, so it absorbs the heat more quickly and become very hot during a day. In night, it radiate heat more quickly and become cold more quickly during night.

9.4 Why conduction of heat does not take place in gases?

Conduction takes place by vibrating atoms and free electrons. As molecules in gases are farther in gases so conduction of heat does not take place in gases

9.5 What measures do you suggest to conserve energy in houses?

Following measures may be taken to save energy.

Hot water tanks are insulated by plastic or foam lagging.
Wall cavities are filled with plastic foam or wool.
Ceiling of rooms is covered by insulating materials (false ceiling).
Double glazed window panes are used. These window panes have air between glass sheets that provides good insulation.

9.6 Why transfer of heat in fluids takes place by convection?

Transfer of heat by actual movement of molecules from hot place to a cold place is known as convection. Convection takes place in fluids because molecules can flow from one place to another.

9.7 What is meant by convection current?

Gases expand on heating, thus convection currents are easily set up due to the differences in the densities of air at various parts in the atmosphere.

9.8 Suggest a simple activity to show convection of heat in gases not given in the book.

Turn on an oven and leave it on for a while. Then turn it off and open the door and feel the heat. If we are not near the oven it will still be warm. This heat is caused by the warm air moving out of the oven and into the cooler surroundings.

9.9 How does heat reach us from the Sun?

Heat energy from sun reaches us neither by conduction nor by convection, because the space between the sun and the Earth’s atmosphere is empty. There is a third mode called radiation by which heat travels from one place to another. It is through radiation that heat reaches us from the sun.

9.10 How various surfaces can be compared by a Leslie cube?

A Leslie cube is a metal box having faces of different nature as shown in figure. The four faces of Leslie’s cube may be as following:

A shining silvered surface
A dull black surface
A white surface
A coloured surface

Hot water is filled in the Leslie’s cube and is placed with one of its face towards a radiation detector. It is found that black dull surface is good emitter of heat.

The rate at which various surfaces absorb heat also depends upon the nature of those surfaces.

A polished surface is poor absorber of heat as its temperature rises very slowly. The observations made from the above experiment are given in the table given below.

Surfaces	Emitter	Absorber	Reflector
Dull black surface	Best	Best	Worst
Coloured surface	Good	Good	Bad
White surface	Bad	Bad	Good
Shining slivered surface	Worst	Worst	Best

9.11 What is greenhouse effect?

Green House:

Green house is a house formed by the glass and transparent polythene sheets. It is used for the better growth of some plants.

Working of Green House:

Light from the sun contains thermal radiations (infrared) of long wavelengths as well as light and ultraviolet radiations of short wavelengths. Glass and transparent polythene sheets allow radiations of short wavelength to pass through easily but not long wavelengths of thermal radiations. Thus, a greenhouse becomes a heat trap. Radiations from the sun pass easily through glass and warms up the objects in the green house. These objects and plants give out radiation of much longer wavelengths. Glass and transparent polythene sheet do not allow them to escape out easily and are reflected back in the greenhouse. This maintains the inside temperature of the green house. Greenhouse effect promises better growth of some plants.

9.12 Explain the impact of greenhouse effect in global warming.

Carbon dioxide and water also behave in a similar way to radiations as glass or polythene. Earth’s atmosphere contains carbon dioxide and water vapours. It causes greenhouse effect and thus maintain the temperature of the earth. During the recent years, the percentage of carbon dioxide has been increased considerably. This has caused an increase in the average temperature of the Earth by trapping more heat due to greenhouse effect. This phenomenon is known as Global warming. This has serious implications for the global climate changes.