Chapter 4

PARAMOUNT SCHOOL SYSTEM

Subject: Physics – I

Unit 4: Dynamics II

MULTIPLE CHOICE QUESTIONS

QI. Choose the best possible option.

  1. A seesaw balances perfectly with two children of equal weight sitting at equal distances from the fulcrum. If one child moves closer to the fulcrum:

    A. The seesaw remains balanced.

B. The seesaw tips towards the child who moved closer.

C. The seesaw tips towards the child who stayed further away.

D. The seesaw topples.

  1. When line of action of the applied force passes through its pivot point then moment of force acting on the body is:

    A. maximum B. minimum C. zero D. infinite

  2. If a body is at rest or moving with uniform rotational velocity, then torque acting on the body will be:

    A. maximum B. minimum C. zero D. infinite

  3. A body in equilibrium must not have:

    A. speed B. quantity of motion C. velocity D. acceleration

  4. A uniformly rotating fan is said to be in:

    A. static equilibrium only B. dynamic equilibrium only

C. both in static and dynamic equilibrium D. not in equilibrium

  1. You throw a weighted fishing net into a calm lake. As the net sinks, it opens fully underwater, spreading out its mesh evenly. Compared to the moment it left your hand, where is the net’s center of mass now?

    A. Higher in the water column.

B. Lower in the water column.

C. At the same depth but slightly shifted horizontally.

D. Unchanged from its position when thrown.

  1. A tightrope walker is carrying a long pole while walking across a rope. The stability of the walker is affected if the pole is:

    A. long and placed vertically

B. long and placed horizontally

C. short and placed vertically

D. short and placed horizontally

  1. It is more difficult to walk on a slippery surface than on a non-slippery one because of:

    A. reduced friction

B. increased friction

C. high grip

D. lower weight

  1. For an object moving with terminal velocity, its acceleration:

    A. Increases with time

B. decreases with time

C. is zero

D. first increases then decreases

  1. The correct order of comparison for the terminal speeds of a raindrop, snowflake, and hailstone is:

    A. Raindrop > Snowflake > Hailstone

B. Hailstone > Raindrop > Snowflake

C. Snowflake > Raindrop > Hailstone

D. Raindrop = Snowflake = Hailstone

  1. You are trying to loosen a nut using a spanner, but it is not working. In order to open the nut, you need to:

    A. Insert a pipe to increase length of spanner

B. use a spanner of small length

C. use plastic and soft spanner

D. tie a rope with spanner

  1. The force that always changes direction of velocity and not its magnitude is called:

    A. gravitational force

B. electric force

C. centripetal force

D. friction

  1. The reason that a car moving on a horizontal road gets thrown out of the road while taking a turn is:

    A. the reaction of the ground

B. rolling friction between tyre and road

C. gravitational force

D. lack of sufficient centripetal force

  1. A car drives at steady speed around a perfectly circular track.

    A. The car’s acceleration is zero.

B. The net force on the car is zero.

C. Both the acceleration and net force on the car point outward.

D. Both the acceleration and net force on the car point inward.

  1. A satellite of mass ‘m’ is revolving around the earth with an orbital speed V. If mass of the satellite is doubled, its orbital speed will become:

    A. double B. half C. one fourth D. remain the same

SHORT RESPONSE QUESTIONS

QII. Give a short response to the following questions

1. Why long spanner is used to open or tight nuts of vehicle’s tyre? While tightening a small nut, extra-long wrench is not suitable. Why?

A long spanner is used to open or tighten a vehicle’s tyre nuts because the longer moment arm allows for greater torque, making it easier to turn the nut with less effort. However, for smaller nuts, an extra-long wrench is not suitable because it may generate excessive torque, which could damage the nut or make it difficult to control the tightening accurately.

2. Why door knobs are fixed at the edge of door? What will happen it the door knob is at the middle of the door?

Door knobs are fixed at the edge of the door to maximize the moment arm, making it easier to apply enough torque to open or close the door. If the door knob were placed in the middle, the shorter moment arm would require more force to produce the same turning effect.

3. If you drop a feather and a bowling ball from the same height, which one will reach the terminal velocity first? Which one of them will hit the ground first?

The feather will reach terminal velocity first because its terminal speed is lower due to air resistance. However, the bowling ball will hit the ground first because its higher mass and greater terminal velocity allow it to fall faster than the feather.

4. Why do ice skates effortlessly slide on ice, while your shoes cause skidding?

Ice skates slide effortlessly on ice because the thin blades reduce friction by creating a thin layer of water under the skate due to pressure. On the other hand, shoes have a larger surface area and more friction, which causes skidding instead of smooth sliding.

5. Explain why it’s easier to push a car on flat tyres than inflated ones. What happens to the frictional force between the tyres and the road?

It’s easier to push a car on flat tyres because the flattened tyres increase the contact area with the road, which reduces pressure at each point, making it easier to push initially. However, this also increases the rolling resistance between the tyres and the road, making it harder to maintain motion compared to inflated tyres that have less contact area and thus less rolling resistance.

6. When standing on a crowded school bus, which stance would provide better stability and prevent you from being pushed over: legs joined or legs spread apart?

Standing with our legs spread apart provides better stability on a crowded school bus because it increases our base of support, making it harder to topple over. This wider stance lowers the chances of losing balance when the bus moves or if you are pushed.

7. Why a moving bicycle is easier to balance? Relate this to the principles of rotational motion.

A moving bicycle is easier to balance because of the principles of rotational motion and angular momentum. When the wheels of the bicycle are in motion, they generate angular momentum, which resists changes in their orientation. This stability helps keep the bicycle upright, making it easier to balance while moving. The faster the wheels rotate, the greater the angular momentum, and the more stable the bicycle becomes.

8. Why is a pencil standing on its tip unstable, and what factors affect the stability of an object balanced on a point?

A pencil standing on its tip is unstable because its center of mass is high and any small disturbance causes the center of mass to fall and the pencil toppling over.

Factors affecting the stability of an object balanced on a point:

  • Center of Mass (CM): Lower CM increases stability; higher CM decreases stability.
  • Area of Support: Larger support area enhances stability; smaller area reduces it.
  • Moment of Force: Weight distribution affects how moments counteract displacement; balanced moments lead to stability.
  • Height of the Pivot Point: Higher pivot points decrease stability.

9. While driving what happens if the driver take the curve too fast? How does centripetal force play a role in keeping the car from skidding off the road?

If a driver takes a curve too fast, the centripetal force required to keep the car moving in a circular path may not be sufficient. This can cause the car to skid outward due to inertia, as the frictional force between the tires and the road may not be enough to provide the necessary centripetal force. Without enough centripetal force, the car loses its ability to follow the curve and will skid off the road.

10. Consider a situation where you swing a ball connected to a string in a circle. How does the tension in the string vary as the ball moves across different points in its circular path, and what forces are involved?

As the ball moves in its circular path, the tension in the string remains relatively constant if the speed is uniform. However, the direction of the tension force always acts toward the center of the circle, providing the necessary centripetal force to keep the ball in circular motion. Gravitational force acts downward on the ball, but it does not affect the tension directly in uniform circular motion.

11. Why is it important for communication satellites in geostationary orbit to maintain a specific speed?

Communication satellites in geostationary orbit need to move at a specific speed to stay directly above the same spot on Earth. This allows them to provide constant communication. If they go too fast or too slow, they would move away from their assigned position or fall back to Earth.

LONG RESPONSE QUESTIONS

QIII. Give a an extended response to the following questions

1. Differentiate between like and unlike parallel forces.

Like Parallel Forces Unlike Parallel Forces
Forces act in the same direction. Forces act in opposite directions.
Resultant force is the sum of the magnitudes of the forces. Resultant force is the difference between the magnitudes of the forces.
Increases the overall force applied on the object, making it easier to move. Can either increase or decrease the overall force, depending on the relative magnitudes.
Example: Pushing a cart with both hands in the same direction. Example: Applying force with both hands on a bike handle, where one hand exerts more force than the other.

2. What is moment of force or torque? On what factors it depends? Write its mathematical formula

Moment of Force or Torque:

Moment of force or torque is the turning effect produced by a force applied on an object about a fixed point or axis of rotation. It causes the object to rotate or spin.

Moment of force or torque is a vector quantity and have the SI unit as Nm.

The moment of force depends on two factors:

  • The magnitude of the force applied.
  • The perpendicular distance from the axis of rotation to the line of action of the force or the moment arm.

The mathematical formula for moment of force is:

Where F is the applied force and d is the perpendicular distance from the axis of rotation to the line of action of the force or the moment arm.

3. Define center of mass. What is effect of mass distribution in a body on its center of mass?

Center of Mass:

The center of mass is the point in a rigid body where its mass is equally distributed, and it behaves as if the entire mass is concentrated at that point.

Effect of Mass Distribution:

The distribution of mass in a body affects its center of mass. In symmetrical objects like spheres or cubes, the center of mass is located at the geometric center. However, in irregular objects or objects with non-uniform mass distribution, the center of mass may not lie at the geometric center and can shift based on how the mass is spread across the object.

4. What is center of gravity? Where will be center of gravity of these regular shaped bodies; circular plate, rectangular and square shaped plate, triangular shaped plate, cylinder, sphere (also draw figures to support your answer). Differentiate between center of mass and center of gravity.

Center of Gravity:

The center of gravity is the point in a body where the entire weight of the object appears to act. It is closely related to the center of mass, especially for uniform gravitational fields, where the two points coincide. However, the center of gravity may differ from the center of mass in cases where gravitational acceleration varies across the body, such as tall structures or at great heights.

Center of Gravity of Regular Shaped Bodies:

Circular Plate The center of gravity is located at the center of the plate.
Rectangular Plate The center of gravity is located at the intersection of the diagonals, which is at the center of the rectangle.
Square Plate Similar to the rectangular plate, the center of gravity is at the center of the square.
Triangular Plate The center of gravity is located at the centroid, which is one-third the height from the base.
Cylinder The center of gravity is at the center of the circular bases.
Sphere The center of gravity is at the geometric center of the sphere.

Difference between Center of Mass and Center of Gravity:

Center of Mass (CM) Center of Gravity (CG)
The point where the mass of an object is equally distributed. The point where the total weight of an object appears to act.
Depends entirely on the mass distribution of the object. Depends on both mass distribution and the gravitational field.
Remains constant for symmetrical objects in a uniform gravitational field. Can change location based on the object’s orientation and the gravitational field.
Determined mathematically or experimentally based on mass distribution. Can be found by balancing the object or using the plumb line method.
Example: Geometric center of a uniform object (e.g., cube, sphere). Example: Can differ for tall or irregular objects in a non-uniform gravitational field.

5. How can you find center of gravity of an irregular shaped thin sheet of plastic?


Take an irregular piece of cardboard. Make holes A, B and C as shown in figure near its edge. 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.

6. What is equilibrium? Describe the conditions of equilibrium. State an explain principle of moments.

Equilibrium:

Equilibrium is the state of an object in which all individual forces and moments of forces (torques) acting upon it are balanced. In this state, the net force and net torque on the object are zero, meaning the object will either remain at rest or move with a constant velocity without any rotational change.

Conditions of Equilibrium:

There are two conditions that must be satisfied for complete equilibrium:

First Condition of Equilibrium:

The vector sum of all forces acting on the body must be zero. This prevents the object from moving in any direction. Mathematically, if is the sum of forces then,

This condition is also known as translational equilibrium.

Example:

Consider a book resting on a table. The weight of the book is balanced by the upward normal force exerted by the table.

Second Condition of Equilibrium:

The vector sum of all torques acting on the body must be zero. This prevents the object from rotating or ensures that it rotates with uniform angular velocity. Mathematically, if is the sum of torques then,

This condition is also known as rotational equilibrium.

Example:

Consider a seesaw with a pivot in the center. The seesaw to be in equilibrium according to the second condition of equilibrium when the clockwise moments must equal to the anticlockwise moments.

For complete equilibrium, both conditions must be satisfied.

Principle of Moments:

The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any pivot point must be equal to the sum of the anticlockwise moments about the same pivot.

Clockwise moments = Anticlockwise moments

Mathematically:

For example, if a uniform meter stick is balanced on a pivot with weights on either side, the moments due to these weights can be balanced by adjusting the distance of the weights from the pivot. This can be verified by the following equation:

Where ​ and ​ are the weights, and ​ and ​ are the respective distances from the pivot. If this equation holds true, the object will remain in equilibrium.

7. Propose how the stability of an object can be improved. Illustrate the applications of stability physics in real life.

Stability of an object can be improved by:

Lowering the center of mass: Objects with a lower center of mass are more stable and less likely to topple over. For instance, sports cars are designed with a low center of gravity to enhance stability during high-speed turns.

Increasing the area of support (base area): A wider base makes an object more stable. This principle is used in designing tripods, where the wide base prevents the camera from toppling over.

Positioning the center of mass directly beneath the point of support: This ensures that any displacement creates a restoring moment, which brings the object back to its original position, as seen in self-righting toys.

Applications of Stability Physics in Real Life:

Racing Cars: Racing cars have a low center of gravity and a wide base to prevent tipping during sharp turns, enhancing safety and performance.

Tall Structures: Skyscrapers are built with a strong, wide foundation and a low center of mass to maintain stability against wind and seismic forces.

Furniture: Chairs and tables are designed with a wide base to prevent them from tipping over easily.

Ships: Ships are built with heavy ballast at the bottom to lower the center of gravity, ensuring stability even in rough waters.

Self-righting Toys: Toys like wobbling dolls have their center of mass below the point of support, making them return to their original position when tilted.

8. Define force of friction. What causes friction? What are advantages and disadvantages of friction? Explain with examples. How can friction be reduced?

Friction:

Friction is the resistance to relative motion that occurs when two surfaces are in contact with each other.

Friction is a vector quantity.

SI unit of friction is the newton (N).

Causes of Friction:

Friction is caused by the roughness of surfaces in contact. Even surfaces that appear smooth have microscopic bumps and irregularities. When these surfaces come into contact, their microscopic roughness interlocks, which resists motion and creates friction. The force required to overcome this interlocking is the frictional force.

Advantages of Friction:

  • Friction between the soles of our shoes (or feet) and the ground allows us to walk without slipping.
  • Friction between tyres and the road surface helps cars move and stop safely.
  • Friction keeps screws and nails in place within wood or other materials, preventing them from loosening.
  • Friction between a pen or pencil and paper allows us to write.

Disadvantages of Friction:

  • Friction opposes the motion of objects, which can make moving objects come to a stop.
  • Friction between moving parts in machinery causes them to heat up, which can lead to damage or energy loss.
  • Friction causes the surfaces of materials, like tires or machine parts, to wear out over time, leading to replacement and maintenance costs.

Methods to Reduce Friction:

  • Polishing: Smoothing out rough surfaces reduces the interlocking of surface irregularities, leading to less friction.
  • Ball bearings: Ball bearings reduce friction by converting sliding motion into rolling motion, which requires less force.
  • Lubricants: Applying oil or grease between surfaces creates a smooth layer that reduces the contact between surfaces, decreasing friction. For example, oil is used in engines to reduce friction between metal parts.

9. Compare rolling friction and sliding friction. How are they different in terms of contact surfaces, motion, and forces involved? Explain with examples.

Rolling friction and sliding friction differ in many ways.

Rolling Friction

Rolling friction is the resistive force that opposes the motion when a body rolls over a surface.

Contact Surfaces:

When an object rolls, only a small portion of the surface is in contact with the ground at any given time, as seen with wheels or spherical objects.

Motion:

Occurs when an object rolls over a surface, such as the wheels of a car or a ball moving across a field. The object rolls without slipping, and the friction opposes the rolling motion.

Forces Involved:

The force of rolling friction is generally much smaller than sliding friction, making it easier to move objects. This is why wheels are commonly used in vehicles, as they reduce the effort needed to move.

Examples:

Pushing a trolley with wheels is easier because of rolling friction.

Sliding Friction

Sliding friction is the resistive force that opposes the motion when two objects slide against each other.

Contact Surfaces:

In sliding, a larger portion of the surfaces of both objects are in continuous contact, like when dragging a box across the floor.

Motion:

Happens when an object slides across a surface, as with pushing a book along a table. The surfaces rub against each other, creating more resistance compared to rolling.

Forces Involved:

Sliding friction is stronger because of the larger contact area and interlocking of surface irregularities. More force is required to overcome sliding friction, as seen when dragging a heavy object on the ground.

Example:

Pushing a heavy box across the floor is harder due to sliding friction.

10. Analyse the dynamics of an object reaching terminal velocity.

When an object falls through a fluid like air, it experiences two main forces:

Gravitational force (weight): This force pulls the object downward. It is equal to the mass of the object multiplied by the acceleration due to gravity (F = mg).

Drag force (air resistance): This force opposes the downward motion of the object. The drag force increases with the speed of the object and depends on factors like the object’s shape, size, and the density of the fluid.

Initially, when the object begins to fall, the gravitational force is much greater than the drag force, so the object accelerates downward. As the object’s speed increases, the drag force also increases.

Eventually, a point is reached where the drag force becomes equal to the gravitational force. At this point, the net force acting on the object becomes zero, and according to Newton’s First Law of Motion, the object stops accelerating. It continues to fall at a constant speed, known as the terminal velocity.

Examples:

  • A skydiver jumps from a plane and initially accelerates due to gravity. As the skydiver gains speed, the drag force increases. After a certain time, the skydiver reaches terminal velocity, where the speed remains constant until the parachute is deployed.
  • Rain droplets also reach terminal velocity as they fall through the air. This prevents them from continuously accelerating, which is why they fall at a relatively constant speed despite being pulled down by gravity.

11. Define centripetal force. Describe the motion of a body in a circular path under the action of centripetal force.

Centripetal Force:

Centripetal force is the force that pulls an object out of its straight-line path and into a circular path. It acts towards the center of the circular path, allowing the object to maintain its circular motion. This force is necessary because, although the speed of the moving object may remain constant, its direction is continuously changing, leading to a change in velocity and an acceleration known as centripetal acceleration.

Mathematically:

The formula for centripetal force ‘Fc’ acting on an object with mass ‘m’ moving at velocity ‘v’ in a circular path of radius ‘r’ is given by:

Description of Motion under Centripetal Force:

In uniform circular motion, the object travels around a circular path at a constant speed. The acceleration is always directed towards the center of the circle, indicating that there is an unbalanced force acting on the object.

For example, when a communications satellite moves in a circular orbit around the Earth, it requires an unbalanced force to keep it in that path. This unbalanced force is the gravitational force acting on the satellite, providing the necessary centripetal force.

Examples:

  • A ball swung on a string experiences tension as centripetal force, pulling it into a circular path.
  • The gravitational force acts as centripetal force for planets orbiting the sun and the moon orbiting the Earth.

12. Identify different sources of centripetal force in real life examples.

Different sources of centripetal force in real-life examples from the provided text include:

Gravitational Force:

In the case of planets orbiting the sun, the gravitational force acts as the centripetal force. For example, the Earth’s orbit around the sun is maintained by the gravitational attraction between the two.

Similarly, the moon orbits the Earth because of the gravitational force exerted by the Earth, which acts as the centripetal force.

Tension:

When a ball is swung in a circle using a string, the tension in the string provides the centripetal force needed to keep the ball moving in a circular path. The tension pulls the ball inward, preventing it from moving in a straight line.

Friction:

When a car turning around a curve on a road, the friction between the tyres and the road provides the centripetal force. This frictional force prevents the car from sliding out of its circular path.

13. Define orbital velocity. How do scientists use the concept of orbital speed to launch satellites into specific orbits? What factors influence the chosen speed?

Orbital velocity of the body is the speed at which it orbits around the center of the system. This System is usually around a massive body.

Mathematically:

The relationship between speed, distance and time is:

In one orbit a satellite travels a distance equal to the circumference of a circle the shape of the orbit. This is equal to ” where ‘r’ is the radius a circle, thus:

The time it takes for an object to orbit around another object is called its orbital period ‘T’. Earth completes its orbital period around the sun every 365 days.

Putting these values in :

This means that for particular distance from the center of earth, all the satellite should have the same orbital speed Irrespective of the size of satellite.

Orbital Speed to Launch Satellites:

To launch a satellite into a specific orbit, scientists adjust the satellite’s speed and altitude. The satellite is first placed at a high altitude using rockets and then accelerated to the required orbital velocity. If the satellite’s speed is too high, it will escape Earth’s gravitational pull and move away. If it is too low, the satellite will fall back to Earth. By achieving the precise orbital speed, the satellite can maintain a circular or nearly circular path around the Earth.

Factors Influencing the Chosen Speed:

  • Altitude (Distance from the Earth): Higher altitudes require lower speeds because the gravitational force is weaker at greater distances. Satellites in lower Earth orbits need higher speeds.
  • Gravitational Force: The mass of the Earth (or the central body) plays a key role. The stronger the gravitational pull, the higher the orbital velocity needed to keep the satellite in orbit.
  • Type of Orbit: The chosen speed depends on the type of orbit (circular, elliptical, etc.). For a stable circular orbit, the speed must remain constant. For elliptical orbits, the speed varies depending on the satellite’s distance from the Earth.