Chapter 3

PARAMOUNT SCHOOL SYSTEM

Subject: Physics – I

Unit 3: Dynamics – I

Exercise

QI. Choose the best possible option.

  1. Inertia of a body is related to which of the following quantities

    A. mass B. force C. weight D. friction

  2. A force of 5N is applied to a body weighing 10 N. Its acceleration in m/s² is:

    A. 0.5 B. 2 C. 5 D. 50

  3. SI unit of linear momentum is:

    A. kg m-1s-1 B. kg m2s-1 C. N m D. kg ms-1

  4. The rate of change of momentum of a free falling body is equal to its:

    A. momentum B. velocity C. Weight D. size

  5. Change in momentum of a body is equal to:

    A. (force) (velocity) B. (force) (time) C. (mass) (time) D. force

  6. A book of mass 5 kg is placed on the table, the magnitude of net force acting on the book is:

    A. 50 N B. 5N C. 25 N D. 10 N

  7. Thrust force is a consequence of which law of motion:

    A. First B. Second C. Third D. Fourth

  8. A force acts on a body for 2 seconds and it produces 50 kgm/s change in its momentum. The force acting on the body is:

    A. 100 N B. 50 N C. 25 N D. 2 N

  9. At the fairground, the force that balances your weight is:

    A. gravitational force B. centripetal force

C. electrostatic force D. frictional force

  1. When a hanging carpet is beaten by a stick, dust flies off the carpet. It is mainly due to:

    A. Action force on carpet B. Reaction force by carpet

C. Inertia of dust D. Rate of change of momentum of carpet

  1. A bucket with water is revolved in a vertical circle. The water does not spill out, even when the bucket is upside down, due to:

    A. Weight of water B. Centrifugal force on water

C. Inertia of water D. Action and Reaction balance each other

  1. The force which moves the car is:

    A. Force developed by engine B. Force of friction between road and tyre

C. Weight of car D. Water spilt on the road

  1. N kg-1 is equivalent to:

    A. ms-1 B. ms-2 C. kgms-1 D. Kgs-2

  2. An object of mass 1 kg placed at Earth’s surface experiences a force of:

    A. 1 N B. 9.8 N C. 100 N D. kg m s

  3. Net force on the body falling in air with uniform velocity is equal to:

    A. Weight of the body B. Air resistance on the body

C. Difference of weight of body and air resistance on it D. Zero

SHORT RESPONSE QUESTIONS

QII. Give a short response to the following questions.

Q1. When a motorcyclist hits a stationary car, he may fly off the motorcycle and the driver in the car may get a neck injury. Explain.

When a motorcyclist hits a stationary car, he cannot stop himself due to inertia and continues in his state of motion, causing him to fly off the motorcycle. Meanwhile, the driver in the car is initially at rest. When the motorcyclist collides with the car, the upper part of the driver’s body tends to remain at rest due to inertia, while the lower part moves forward with the car due to the force of the collision. This mismatch in motion can result in a neck injury for the driver.

2. In autumn, when you shake a branch, the leaves are detached. Why?

Inertia causes the leaves to detach when the branch is shaken. The leaves tend to remain at rest while the branch moves, and this difference in motion breaks the weak connection between the leaves and the branch, causing them to fall.

3. Why it is not safe to apply brakes only on the front wheel of a bicycle?

Applying brakes only on the front wheel of a bicycle can lead to an unbalanced force that causes the bicycle to tip forward. This occurs because of inertia, where the back part of the bicycle continues to move forward while the front part stops suddenly, causing the rider to fall over the handlebars and lose control.

4. Deduce Newton’s first law of motion form Newton’s second law of motion.

According to Newton second law of motion, The acceleration of an object as produced by a net force is directly proportional to t the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

It can be mathematically expressed as:

According to Newton’s first law, an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity unless acted upon by an unbalanced force. If there is no net force acting on the object, the acceleration (a) will be zero.

This indicates that when no net external force is acting on an object, the net force is zero.

5. Action and reaction are equal but opposite in direction. These forces always act in pair. Do they balance each other? Can bodies move under action – reaction pair?

No, action and reaction forces do not balance each other because they act on different objects. Bodies can still move under an action-reaction pair, as the forces are exerted on separate objects, allowing them to move in opposite directions. For example, when we walk, our foot pushes backward on the ground (action), and the ground pushes forward on our foot (reaction). This forward reaction force helps us move ahead.

6. A man slips on the oily floor; he wants to move out of this area. He is alone. He throws his bag to move out of this slippery area. Why is it so?

The man throws his bag to move out of the slippery area due to Newton’s third law of motion. When he throws the bag, the action force pushes the bag in one direction, and the reaction force pushes him in the opposite direction, helping him move away from the slippery area.

7. How would you use Newton’s 3rd law of motion and law of conservation of momentum to explain motion of rocket?

Newton’s 3rd law of motion states that every action has an equal and opposite reaction. In a rocket, the action is the expulsion of gas downwards, and the reaction is the rocket moving upwards. The law of conservation of momentum explains that as the gas is pushed out with momentum in one direction, the rocket gains equal momentum in the opposite direction, propelling it forward.

8. Why are cricket batter gloves padded with foam?

Cricket batter gloves are padded with foam to reduce the impact of the ball. The padding increases the time of contact between the ball and the hand, which decreases the force experienced, protecting the hands from injury.

9. Where will your weight be greater, near earth or near moon? What about mass?

Our weight will be greater near Earth because Earth has a stronger gravitational pull compared to the Moon. Weight is the force exerted by gravity on an object, which means it varies with the gravitational field strength. In contrast, our mass remains constant regardless of your location; it is the measure of the amount of matter in our body and does not change whether we are on Earth or the Moon.

10. When Ronaldo kicks the ball, at the highest point of ball both Earth and ball attract each other with the same magnitude of force. Why then the ball moves towards Earth and not the Earth?

When Ronaldo kicks the ball, both the Earth and the ball exert equal gravitational forces on each other due to Newton’s third law of motion. However, the ball moves toward the Earth because of its much smaller mass compared to the Earth. According to the law of conservation of momentum, the acceleration of the ball is greater than that of the Earth, causing it to fall toward the Earth instead of the Earth moving toward the ball.

LONG RESPONSE QUESTIONS

QIII. Give a an extended response to the following questions

1. State first law of motion. Explain with the help of examples. Why is it called law of inertia?

Newton’s First Law of Motion states that an object at rest will remain at rest, and an object in motion will continue to move with constant velocity unless acted upon by an external unbalanced force.

Examples:

  • In a soccer game, when a ball is kicked, it keeps rolling until friction or another force stops it. Without external forces, it would continue moving in a straight line.
  • If we are standing in a moving bus, when the bus suddenly starts or stops, we feel a push backward or forward because our body tends to maintain its state of rest or motion.

Law of Inertia:

This law is also called the law of inertia because inertia is the tendency of objects to resist changes in their state of rest or uniform motion. Objects with more mass have more inertia, making it harder to change their motion. For example, a large man on a swing is harder to push or stop than a small child because the larger man has greater inertia.

2. Define inertia. Why is it important to have knowledge of inertia in our daily life? Elaborate your answer with examples.

Inertia is the tendency of objects to resist changes in their state of rest or uniform motion. Objects with more mass have more inertia, making it harder to change their motion.

Importance of Inertia:

Understanding inertia helps us predict how objects will behave in different situations, which is crucial for safety and efficiency in everyday activities.

Examples:

Driving a car: When a car suddenly stops, passengers tend to lunge forward because their bodies were in motion, showing inertia. Wearing seat belts helps counteract this by restraining motion, ensuring safety.

Bus travel: While standing in a moving bus, if the bus suddenly stops, passengers feel a forward push due to inertia, as their bodies want to continue moving.

Pushing heavy objects: Moving a large object like a sofa is harder because it has more mass, and thus more inertia, compared to a lighter chair.

Having knowledge of inertia helps us to plan actions and responses accordingly.

3. State and prove Newton’s second law of motion. Deduce Newton’s second law of motion from its first law?

Statement:

The acceleration of an object as produced by a net force is directly proportional to t the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Derivation:

The greater the applied net force on an object, the greater its acceleration. If you double the force, the acceleration also doubles, showing that acceleration is proportional to force

For the same force, if the mass of the object increases, its acceleration decreases.

By combining these relationships, we get the formula:

​

Example:

If we apply the same force to a small object like a ball and a large object like a car, the ball will accelerate more due to its smaller mass.

Deduction of Newton’s Second Law of Motion:

According to Newton’s first law, an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity unless acted upon by an unbalanced force. If there is no net force acting on the object, the acceleration () will be zero.

This indicates that when no net external force is acting on an object, the net force is zero.

4. State Newton’s 3rd law of motion. Explain with examples from daily life.

Statement:

For every action, there is an equal and opposite reaction.

Explanation:

When one object exerts a force on another object, the second object exerts an equal force in the opposite direction on the first object. These forces are called action-reaction pairs, and they always act on different objects, so they do not cancel each other out.

Examples from Daily Life:

  • Kicking a football: When you kick a football, your foot exerts a force (action) on the ball, and the ball exerts an equal and opposite force (reaction) on your foot. This is why you can feel the impact.
  • Walking: As you push against the ground with your legs (action), the ground pushes back with an equal and opposite force (reaction), allowing you to move forward.
  • Rocket launch: The exhaust gases are pushed downward (action), and the rocket is pushed upward with an equal force (reaction), allowing it to lift off.

5. State the limitations of Newton’s laws of motion.

Limitations of Newton’s Laws of Motion:

Limitations of Newton’s Laws of motion are:

  • Newton’s laws do not work well at the atomic or subatomic levels. At this scale, quantum mechanics becomes more relevant, and concepts like position and acceleration are not well defined.
  • Not valid for objects at high speeds: Newton’s laws fail for objects moving close to the speed of light. In these cases, relativistic effects need to be considered, and Einstein’s theory of relativity takes over.

6. Differentiate with examples between contact and non-contact forces. Also, explain fundamental forces and the role of Dr. Abdus Salam from Pakistan in unifying two fundamental forces.

Contact Forces:

These forces occur when two objects are physically in contact.

Examples:

  • Normal Force: A book resting on a table experiences a normal force perpendicular to the table surface.
  • Friction Force: A moving car experiences friction between its tires and the road.
  • Thrust Force: The force generated by an engine to propel a car forward.
  • Tension Force: The force in a rope when it pulls an object upwards.

Non-Contact Forces:

These forces act without direct physical contact between objects.

Examples:

  • Gravitational Force: The force exerted by the Earth on the Moon.
  • Electrostatic Force: The attraction between a positively charged object and a negatively charged object.
  • Magnetic Force: The repulsion between two like poles of a magnet.

Fundamental Forces in Nature:

Strong Nuclear Force:

Strength: Strongest fundamental force.

Function: Holds protons and neutrons together in atomic nuclei, overcoming their repulsion.

Mediators: Exchange particles called pions.

Range: Very short, approximately the diameter of a proton.

Electromagnetic Force:

Strength: Second strongest force.

Function: Acts between charged particles, causing attraction or repulsion.

Mediators: Massless particles known as photons.

Range: Infinite; strength diminishes with distance but can be significant.

Gravitational Force:

Strength: Weakest of the four forces.

Function: Attraction between all objects with mass, influencing their motion (e.g., keeping planets in orbit).

Mediators: Theorized to involve massless particles called gravitons (not yet detected).

Range: Infinite; noticeable mainly with large masses.

Weak Nuclear Force:

Strength: Weaker than the strong nuclear force, about 10,000 times weaker.

Function: Responsible for processes like radioactive decay and changing particle types.

Mediators: Vector bosons (W and Z).

Range: Very short, limited to subatomic distances.

Role of Dr. Abdus Salam:

Dr. Abdus Salam, a Pakistani physicist, played a crucial role in the unification of the electromagnetic and weak nuclear forces, known as the electroweak theory. This theory showed that these two forces are manifestations of the same fundamental force, a major milestone in modern physics. Dr. Salam, along with Steven Weinberg and Sheldon Glashow, was awarded the Nobel Prize for this groundbreaking work.

7. Represent the forces acting on a body using free body diagrams.


A free-body diagram (FBD) is a schematic representation that focuses on a single object being analyzed, showing all the forces acting on it.

It helps study forces and their effects on the object.

Arrows indicate the forces acting on the object, with their lengths proportional to the magnitudes of the forces.

Each force is labeled with the symbol followed by a subscript, such as:

  • ​: Force of gravity.
  • ​: Normal force.
  • ​: Friction.
  • ​: Tension.
  • : Applied force.

FBDs are essential for analyzing the interactions affecting the motion of the object.

8. Define momentum. What is its formula and unit? Is it a scalar or vector quantity? Show that units of momentum, Ns and kgm/s are equal.

Definition:

Momentum is defined as the product of an object’s mass and its velocity.

It is denoted by the symbol .

Formula:

Where m is the mass and is the velocity.

Unit: The SI unit of momentum is kilogram-meter per second (kgm/s) or newton-second (Ns).

Type: Momentum is a vector quantity.

Proof:

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

Multiplying both sides by “s” we get

9. Differentiate between mass and weight of body.

Mass Weight
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.
Mass is scalar quantity. Weight is a vector quantity.
Mass is measured by physical balance. Weight is measured by spring balance.
Mass of body remains uniform everywhere. Weight of body varies depending upon the value of “g”.
Its formula is m = F/a Its formula is w = mg.
Its SI unit is kilogram. Its SI unit is Newton.

10. What are gravitational field and gravitational field strength? Explain.

Gravitational Field:

Gravitational field refers to the region surrounding a massive object (like Earth or the Sun) where gravitational forces can be felt by other objects. In this field, objects experience a force of attraction toward the massive body.

Gravitational Field Strength:

Gravitational field strength is defined as the force per unit mass acting on an object within a gravitational field. It is mathematically expressed as:

According to Newton second law of motion,

Similarly,

Where is the gravitational field strength, is the gravitational force, and is the mass of the object.

  • Gravitational field strength is a vector quantity, pointing in the direction of the gravitational force, typically downward toward the center of the mass.
  • On the surface of Earth, the gravitational field strength is approximately
  • The gravitational field strength decreases as we move away from the Earth’s surface and varies on different planets, resulting in different gravitational field strengths.

11. Justify and illustrate the use of electronic balances to measure mass.

Electronic balances, like force sensors, accurately measure mass by detecting the force exerted on an object due to gravity and converting it into a digital readout. Since weight is the gravitational force (W = mg), these balances indirectly measure mass. They are calibrated to show mass in kilograms, regardless of the gravitational field strength. For example, an 8 kg school bag would have the same mass on both Earth and the Moon, even though its weight changes with gravity.

12. State and prove Newton’s second law of motion in term of momentum.

A force ” produces acceleration ” in a body of mass ‘m’. By Newton’s second law of motion it is written as

…… eq i

The acceleration produced changes the velocity of the body from initial velocity ” to final velocity ” during time interval ”. Then by definition of acceleration

…… eq ii

Putting equation ii in equation i.

The time rate of change of linear momentum of a body is equal to the net force acting on the body.

13. Define isolated system. State law of conservation of linear momentum. Explain with example.

Isolated System:

An isolated system is a group of bodies or particles that interact with each other, but there is no external force acting on them. The system is separated by a boundary, and interactions with the environment do not affect the system.

Law of Conservation of Momentum:

Statement:

The momentum of an isolated system remains constant.

Derivation:

For an isolated system, there is no net force acting, i.e,

Therefore, Newton’s second law in terms of momentum can be written as:

In the absence of external forces, the final momentum of the system must be equal to its initial momentum.

Example:

Consider a gun of mass and a bullet of mass . Before firing, the total momentum is zero. After firing, the bullet moves with velocity in one direction, and the gun recoils with velocity in the opposite direction. The total momentum is still zero, as shown by the equation:

The negative sign indicates that the gun moves in the opposite direction to the bullet. Since the gun’s mass is much larger than the bullet’s, its recoil velocity is much smaller.