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Force and Laws of Motion – CBSE NCERT Study Resources

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Force and Laws of Motion

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9th

9th - Science

Force and Laws of Motion

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Overview of the Chapter: Force and Laws of Motion

This chapter introduces the fundamental concepts of force and the laws governing motion as described by Sir Isaac Newton. Students will learn about the effects of force, types of forces, and the three laws of motion that form the basis of classical mechanics.

Force: A push or pull acting upon an object, resulting from its interaction with another object, which can change the state of motion or shape of the object.

Key Topics Covered

  • Understanding Force and its Effects
  • Balanced and Unbalanced Forces
  • Newton's First Law of Motion (Law of Inertia)
  • Newton's Second Law of Motion
  • Newton's Third Law of Motion
  • Conservation of Momentum

Understanding Force and its Effects

Force can cause an object to start moving, stop moving, change its speed, or change its direction. It can also deform objects. The SI unit of force is the Newton (N).

Balanced Forces: When two equal and opposite forces act on an object, they cancel each other out, resulting in no change in the object's state of motion.

Unbalanced Forces: When forces acting on an object are not equal, they cause a change in the object's state of motion.

Newton's First Law of Motion (Law of Inertia)

An object remains in a state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.

Newton's Second Law of Motion

The rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction of the force. Mathematically, it is expressed as F = ma, where F is force, m is mass, and a is acceleration.

Newton's Third Law of Motion

For every action, there is an equal and opposite reaction. This means that forces always occur in pairs.

Momentum: The product of an object's mass and its velocity (p = mv). It is a vector quantity with both magnitude and direction.

Conservation of Momentum

In an isolated system (where no external forces act), the total momentum before a collision is equal to the total momentum after the collision. This principle is derived from Newton's laws.

Applications of the Laws of Motion

  • Designing safety features in vehicles (e.g., seat belts, airbags)
  • Understanding the motion of rockets and satellites
  • Analyzing sports activities and athlete performance

All Question Types with Solutions – CBSE Exam Pattern

Explore a complete set of CBSE-style questions with detailed solutions, categorized by marks and question types. Ideal for exam preparation, revision and practice.

Very Short Answer (1 Mark) – with Solutions (CBSE Pattern)

These are 1-mark questions requiring direct, concise answers. Ideal for quick recall and concept clarity.

Question 1:
Define force.
Answer:

A push or pull that changes an object's state of motion.

Question 2:
State Newton's First Law of Motion.
Answer:

An object remains at rest or in uniform motion unless acted upon by a force.

Question 3:
What is the SI unit of force?
Answer:

Newton (N).

Question 4:
Give an example of balanced forces from NCERT.
Answer:

A book resting on a table.

Question 5:
What is inertia?
Answer:

The tendency of an object to resist changes in its motion.

Question 6:
Name the force that opposes motion between surfaces.
Answer:

Friction.

Question 7:
State Newton's Second Law of Motion.
Answer:

Force equals mass times acceleration (F=ma).

Question 8:
What happens to acceleration if force is doubled?
Answer:

Acceleration also doubles (if mass is constant).

Question 9:
Give a real-world example of action-reaction pairs.
Answer:

Rowing a boat pushes water backward, moving the boat forward.

Question 10:
State Newton's Third Law of Motion.
Answer:

Every action has an equal and opposite reaction.

Question 11:
What is the momentum of an object?
Answer:

Mass multiplied by velocity (p=mv).

Question 12:
How does seatbelt use relate to inertia?
Answer:

Prevents passengers from moving forward during sudden stops.

Question 13:
Name the force that keeps planets in orbit.
Answer:

Gravitational force.

Question 14:
What is the conservation of momentum?
Answer:

Total momentum remains constant in a closed system.

Question 15:
What is the SI unit of force?
Answer:

The SI unit of force is the newton (N). One newton is defined as the force required to accelerate a mass of 1 kg by 1 m/s².

Question 16:
Give an example where friction is beneficial.
Answer:

Friction is beneficial in walking—it prevents slipping by providing grip between shoes and the ground. It also helps in braking vehicles.

Question 17:
What is the relationship between force, mass, and acceleration as per Newton's Second Law?
Answer:

According to Newton's Second Law, force (F) equals mass (m) multiplied by acceleration (a):
F = m × a.

Question 18:
Define momentum.
Answer:

Momentum is the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.

Question 19:
State the Law of Conservation of Momentum.
Answer:

The Law of Conservation of Momentum states that the total momentum of a closed system remains constant if no external unbalanced force acts on it.

Question 20:
Why do passengers lean forward when a moving bus stops suddenly?
Answer:

Due to inertia, passengers tend to maintain their state of motion even when the bus stops. Hence, they lean forward.

Question 21:
What is the effect of balanced forces on an object?
Answer:

Balanced forces do not change the state of motion of an object. They may cause deformation but do not produce acceleration.

Question 22:
Why is it easier to push an empty box than a heavy box?
Answer:

A heavy box has greater inertia due to higher mass, requiring more force to accelerate it compared to an empty box.

Question 23:
What is the reaction force when a ball hits a wall?
Answer:

As per Newton's Third Law, the wall exerts an equal and opposite reaction force on the ball, causing it to bounce back.

Very Short Answer (2 Marks) – with Solutions (CBSE Pattern)

These 2-mark questions test key concepts in a brief format. Answers are expected to be accurate and slightly descriptive.

Question 1:
Define force and state its SI unit.
Answer:

A force is a push or pull that changes or tends to change the state of rest or motion of an object.
The SI unit of force is newton (N).

Question 2:
State Newton's First Law of Motion with an example.
Answer:

Newton's First Law of Motion states that an object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.
Example: A book lying on a table stays at rest until someone pushes or lifts it.

Question 3:
What is the relationship between momentum and force?
Answer:

Force is the rate of change of momentum.
Mathematically, Force (F) = Change in momentum (Δp) / Time (t).

Question 4:
Why do passengers tend to fall forward when a moving bus stops suddenly?
Answer:

Due to inertia of motion, passengers' bodies tend to stay in motion even when the bus stops.
Their upper body moves forward while their lower body is in contact with the seat, causing them to fall forward.

Question 5:
Differentiate between balanced and unbalanced forces.
Answer:
  • Balanced forces: Equal in magnitude but opposite in direction; no change in motion.
  • Unbalanced forces: Unequal in magnitude; causes acceleration or deceleration.
Question 6:
Calculate the force required to accelerate a 5 kg object at 2 m/s².
Answer:

Using F = m × a:
Mass (m) = 5 kg
Acceleration (a) = 2 m/s²
Force (F) = 5 × 2 = 10 N.

Question 7:
Explain why a cricketer moves his hands backward while catching a fast-moving ball.
Answer:

By moving hands backward, the cricketer increases the time to stop the ball.
This reduces the force exerted on his hands (F = Δp/t), preventing injury.

Question 8:
State the principle of conservation of momentum.
Answer:

The conservation of momentum states that the total momentum of an isolated system remains constant if no external force acts on it.

Question 9:
Why are seat belts used in cars?
Answer:

Seat belts prevent passengers from being thrown forward due to inertia during sudden braking.
They increase stopping time, reducing the impact force on the body.

Question 10:
A 10 N force acts on a 2 kg object. What is its acceleration?
Answer:

Using F = m × a:
Force (F) = 10 N
Mass (m) = 2 kg
Acceleration (a) = F/m = 10/2 = 5 m/s².

Question 11:
Define inertia and give its types.
Answer:

Inertia is the tendency of an object to resist changes in its state of motion.
Types:

  • Inertia of rest
  • Inertia of motion
  • Inertia of direction

Short Answer (3 Marks) – with Solutions (CBSE Pattern)

These 3-mark questions require brief explanations and help assess understanding and application of concepts.

Question 1:
Define inertia and explain its types with examples.
Answer:

Inertia is the property of an object to resist any change in its state of rest or uniform motion. It is directly related to the mass of the object.

  • Inertia of rest: Tendency to remain at rest. Example: A book on a table stays unless moved.
  • Inertia of motion: Tendency to stay in motion. Example: A moving car continues unless brakes are applied.
  • Inertia of direction: Tendency to maintain direction. Example: Passengers lean sideways when a turning bus suddenly changes direction.
Question 2:
State Newton's First Law of Motion and give a real-life application.
Answer:

Newton's First Law of Motion states that an object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.

Application: Seatbelts in cars prevent passengers from jerking forward during sudden brakes due to inertia of motion.

Question 3:
Differentiate between balanced and unbalanced forces with examples.
Answer:
  • Balanced forces are equal and opposite, causing no change in motion. Example: A book on a table (gravity and normal force cancel out).
  • Unbalanced forces cause acceleration. Example: Pushing a toy car makes it move forward.
Question 4:
Explain how momentum is calculated and its SI unit.
Answer:

Momentum (p) is the product of an object's mass (m) and velocity (v):
p = m × v
Its SI unit is kg m/s. Higher momentum means greater force is needed to stop the object.

Question 5:
Describe an activity to demonstrate Newton's Third Law of Motion.
Answer:

Activity: Inflate a balloon and release it without tying.
Observation: The balloon moves forward as air escapes backward.
Explanation: The action (air pushing backward) results in an equal and opposite reaction (balloon moving forward), illustrating Newton's Third Law.

Question 6:
Why do cricketers bend their knees while catching a fast-moving ball?
Answer:

Cricketers bend their knees to increase the time of impact, reducing the force exerted on their hands (F = Δp/Δt). This prevents injury by slowing the ball's momentum gradually.

Question 7:
State Newton’s First Law of Motion and give a real-life application.
Answer:

Newton’s First Law of Motion states that an object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.

Application: Seatbelts in cars prevent passengers from jerking forward during sudden brakes (due to inertia of motion).

Question 8:
Explain how action and reaction forces work in rocket propulsion.
Answer:

Rockets push exhaust gases downward (action), and gases exert an equal upward force (reaction) on the rocket, propelling it forward (as per Newton’s Third Law).

Question 9:
Why do athletes run a few steps before taking a long jump?
Answer:

Athletes run to gain momentum (mass × velocity). Higher velocity increases inertia of motion, allowing a longer jump. Stopping suddenly would reduce the jump distance due to inertia.

Long Answer (5 Marks) – with Solutions (CBSE Pattern)

These 5-mark questions are descriptive and require detailed, structured answers with proper explanation and examples.

Question 1:
Explain Newton’s First Law of Motion with an example from daily life and an NCERT example.
Answer:
Concept Overview

Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by an external force.

Process Explanation
  • Inertia resists changes in motion.
  • Force is needed to alter an object’s state.
Real-world Application

When a bus stops suddenly, passengers jerk forward due to inertia. Our textbook shows a coin on a card experiment where the coin falls into a glass when the card is flicked.

Question 2:
Describe how momentum is conserved in a collision, using an NCERT example.
Answer:
Concept Overview

Momentum (mass × velocity) remains constant in a closed system.

Process Explanation
  • Total momentum before collision = total momentum after.
  • Example: Two balls colliding.
Real-world Application

In car crashes, seat belts reduce momentum gradually. Our textbook shows the example of a gun recoiling when fired, conserving momentum.

Question 3:
What is frictional force? Explain its role in walking with an NCERT example.
Answer:
Concept Overview

Friction opposes motion between surfaces in contact.

Process Explanation
  • Static friction helps us walk without slipping.
  • Kinetic friction slows moving objects.
Real-world Application

Without friction, we would slide. Our textbook shows how rough soles increase grip, like in sports shoes.

Question 4:
Explain Newton’s Second Law mathematically and with a real-world example.
Answer:
Concept Overview

Force equals mass multiplied by acceleration (F = ma).

Process Explanation
  • Greater force increases acceleration.
  • Greater mass reduces acceleration.
Real-world Application

Pushing a shopping cart lightly accelerates it slowly. Our textbook shows how a cricket ball accelerates faster when hit harder.

Question 5:
How does Newton’s Third Law apply to rocket propulsion? Include an NCERT example.
Answer:
Concept Overview

Every action has an equal and opposite reaction.

Process Explanation
  • Rockets push exhaust gases downward.
  • Gases push the rocket upward.
Real-world Application

Jet engines work similarly. Our textbook shows the balloon experiment where air escaping propels the balloon forward.

Question 6:
Explain Newton's First Law of Motion with an example from our textbook and a real-world application.
Answer:
Concept Overview

Newton's First Law states that an object remains in its state of rest or uniform motion unless acted upon by an external force. This is also called the law of inertia.

Process Explanation

Our textbook shows a book on a table staying at rest until pushed. Similarly, a passenger in a moving bus jerks forward when brakes are applied.

Real-world Application

Seatbelts in cars prevent injuries by countering inertia during sudden stops.

Question 7:
Describe how momentum is calculated and give one NCERT example and a real-life scenario.
Answer:
Concept Overview

Momentum (p) is the product of mass (m) and velocity (v), given by p = m × v.

Process Explanation

In our textbook, a cricket ball has higher momentum than a tennis ball when thrown at the same speed due to greater mass.

Real-world Application

A truck moving slowly can have more momentum than a fast-moving bicycle because of its larger mass.

Question 8:
What is conservation of momentum? Explain with the NCERT example of colliding balls.
Answer:
Concept Overview

The total momentum of a system remains constant if no external force acts, as per the conservation of momentum.

Process Explanation

Our textbook shows two balls colliding: the sum of their momenta before and after collision remains equal.

Real-world Application

In rocket propulsion, exhaust gases and the rocket conserve momentum, enabling liftoff.

Question 9:
How does friction affect motion? Use the NCERT example of a rolling ball and a daily-life observation.
Answer:
Concept Overview

Friction opposes motion between surfaces. It slows down moving objects and generates heat.

Process Explanation

Our textbook explains a rolling ball stops due to friction between the ball and ground.

Real-world Application

Brakes in bicycles work by increasing friction between pads and wheels to stop motion.

Question 10:
Differentiate between balanced and unbalanced forces with NCERT and real-world examples.
Answer:
Concept Overview

Balanced forces cancel out, causing no motion, while unbalanced forces change an object's state.

Process Explanation

Our textbook shows a box at rest when equal forces act opposite. Unbalanced forces make it move.

Real-world Application

A tug-of-war team wins when their force becomes unbalanced against the opponents.

Question 11:
Define force and explain its effects with suitable examples. Also, state Newton's First Law of Motion and how it relates to the concept of inertia.
Answer:

Force is defined as a push or pull that changes or tends to change the state of rest or uniform motion of an object. It can alter the speed, direction, or shape of an object.

Effects of Force:

  • Change in Speed: A football speeds up when kicked.
  • Change in Direction: A moving car turns when the driver steers.
  • Change in Shape: A rubber band stretches when pulled.

Newton's First Law of Motion (Law of Inertia): An object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force. Inertia is the tendency of an object to resist changes in its state of motion. For example, a passenger in a moving bus jerks forward when the bus stops suddenly due to inertia.

Question 12:
Explain Newton's Second Law of Motion mathematically and derive the formula F = ma. Also, provide a real-life application of this law.
Answer:

Newton's Second Law of Motion states that the force acting on an object is directly proportional to the rate of change of its momentum.

Derivation:
Momentum (p) = mass (m) × velocity (v)
Force (F) ∝ rate of change of momentum
F ∝ Δp/Δt
If mass is constant, F ∝ m(Δv/Δt)
Since acceleration (a) = Δv/Δt,
F ∝ ma
Thus, F = kma (where k is a constant, taken as 1 for simplicity).
Final formula: F = ma

Real-life Application: A cricket player moves their hands backward while catching a fast ball to reduce the force (by increasing time Δt), preventing injury.

Question 13:
Describe Newton's Third Law of Motion with an example. How does this law explain the motion of a rocket in space?
Answer:

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

Example: When you push a wall, the wall exerts an equal force back on your hand.

Rocket Motion:

  • The rocket engine expels hot gases downward (action).
  • The gases exert an equal and opposite force upward (reaction), propelling the rocket forward.
This law explains how rockets move in space despite the absence of air or other medium, as the action-reaction pair occurs between the rocket and the expelled gases.

Question 14:
A car of mass 1000 kg accelerates uniformly from rest to 20 m/s in 10 seconds. Calculate the force applied by the engine using Newton's Second Law. Also, explain why seatbelts are important during sudden braking.
Answer:

Step 1: Calculate acceleration (a).
Initial velocity (u) = 0 m/s
Final velocity (v) = 20 m/s
Time (t) = 10 s
a = (v - u)/t = (20 - 0)/10 = 2 m/s²

Step 2: Calculate force (F).
Mass (m) = 1000 kg
F = ma = 1000 × 2 = 2000 N

Importance of Seatbelts: Due to inertia, passengers tend to continue moving forward when a car brakes suddenly. Seatbelts provide an opposing force to prevent injuries by stopping the passengers' motion relative to the car.

Question 15:
Explain Newton's First Law of Motion with the help of an example from daily life. How does this law justify the need for wearing seat belts in cars?
Answer:

Newton's First Law of Motion, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This means objects naturally resist changes to their state of motion.

Example: When a bus suddenly stops, passengers tend to jerk forward. This happens because their bodies (due to inertia) continue moving at the bus's previous speed until the seat or another force (like a seat belt) stops them.

Connection to Seat Belts: In a moving car, passengers and the driver share the same velocity as the car. If the car stops abruptly (e.g., during a collision), the passengers' bodies tend to keep moving forward due to inertia. Seat belts provide the necessary external force to stop this motion, preventing injuries by holding the passengers securely to the seat.

Question 16:
Define momentum and derive its SI unit. A car of mass 1000 kg is moving with a velocity of 20 m/s. Calculate its momentum. If the car comes to rest in 5 seconds, what is the magnitude of the force applied by the brakes?
Answer:

Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.

SI Unit Derivation: Momentum = mass × velocity
Mass → kg (kilogram)
Velocity → m/s (meters per second)
Thus, SI unit of momentum = kg m/s.

Given:
Mass (m) = 1000 kg
Velocity (v) = 20 m/s

Momentum Calculation:
Momentum (p) = m × v
p = 1000 kg × 20 m/s
p = 20,000 kg m/s

Force Calculation:
Final velocity (v') = 0 m/s (car comes to rest)
Time (t) = 5 s
Using Newton's Second Law: Force = Change in momentum / Time
F = (mv' - mv) / t
F = (0 - 20,000) / 5
F = -4000 N (negative sign indicates opposing force)

The magnitude of the force applied by the brakes is 4000 N.

Question 17:
Explain Newton's First Law of Motion with the help of an example from daily life. Also, discuss how this law is related to the concept of inertia.
Answer:

Newton's First Law of Motion, also known as the Law of Inertia, states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.


Example from daily life: When a bus suddenly stops, passengers tend to jerk forward. This happens because their bodies (due to inertia) tend to remain in motion even when the bus stops. Similarly, when the bus accelerates, passengers feel pushed backward because their bodies resist the change in motion.


Relation to Inertia: Inertia is the property of an object to resist changes in its state of motion. Newton's First Law directly describes this behavior. The greater the mass of an object, the greater its inertia, making it harder to start or stop its motion.


Additional Insight: Seatbelts in cars are designed to counteract inertia by preventing passengers from moving forward abruptly during sudden stops, demonstrating the practical application of this law in safety measures.

Question 18:
Explain Newton's First Law of Motion with the help of an example from daily life. How does this law relate to the concept of inertia?
Answer:

Newton's First Law of Motion, also known as the Law of Inertia, states that an object at rest stays at rest, and an object in motion continues to move at a constant velocity unless acted upon by an unbalanced force.


Example: When a bus suddenly stops, passengers tend to jerk forward. This happens because their bodies (initially in motion) resist the change due to inertia and continue moving forward until the seatbelt or friction stops them.


Relation to Inertia: Inertia is the property of matter that resists changes in its state of motion. Newton's First Law directly describes this behavior—objects naturally resist acceleration unless a force acts on them.


Additional Insight: Inertia depends on mass—the greater the mass, the higher the inertia. For example, pushing a heavy rock requires more force than pushing a light box because the rock has more inertia.

Question 19:
Explain Newton's First Law of Motion with the help of a real-life example. How does this law justify the need for wearing seatbelts in vehicles?
Answer:

Newton's First Law of Motion, also known as the Law of Inertia, states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.


Real-life example: Imagine a book lying on a table. It remains stationary until someone applies a force to move it. Similarly, a moving car tends to stay in motion unless brakes are applied.


Connection to seatbelts: When a vehicle suddenly stops (due to braking or collision), passengers inside continue moving forward due to inertia. Seatbelts provide the necessary unbalanced force to stop passengers, preventing injuries. Without seatbelts, passengers could be thrown forward, leading to severe accidents.


Value-added insight: Inertia depends on mass—greater mass means greater inertia. This is why heavier objects resist changes in motion more than lighter ones.

Question 20:
Explain Newton's First Law of Motion with the help of an example from daily life. How does this law relate to the concept of inertia?
Answer:

Newton's First Law of Motion, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force.


Example from daily life: When a bus suddenly starts moving forward, passengers standing in the bus tend to fall backward. This happens because their feet (in contact with the bus) move forward with the bus, but the rest of their body tends to stay at rest due to inertia.


Relation to Inertia: Inertia is the property of an object to resist any change in its state of motion. The First Law directly describes this behavior—objects naturally resist changes to their velocity (whether at rest or moving). The greater the mass of an object, the greater its inertia.


Additional Insight: Seatbelts in cars are designed to counteract inertia. During sudden braking, the seatbelt applies an external force to prevent passengers from continuing their forward motion (as per inertia), thereby ensuring safety.

Case-based Questions (4 Marks) – with Solutions (CBSE Pattern)

These 4-mark case-based questions assess analytical skills through real-life scenarios. Answers must be based on the case study provided.

Question 1:
A cricket ball of mass 150g is moving at 20 m/s. A batsman hits it back at 25 m/s. Calculate the change in momentum and identify the force acting if the contact lasts 0.01s.
Answer:
Case Summary

A ball's momentum changes due to a bat's force.


Scientific Principle
  • Change in momentum (Δp) = m(v-u)
  • Force = Δp/t (Newton's 2nd Law)

Solution Approach

Δp = 0.15kg (25-(-20)) = 6.75 kg·m/s. Force = 6.75/0.01 = 675N. Our textbook shows similar calculations for a tennis ball.

Question 2:
A car accelerates from rest to 18 m/s in 6s. If its mass is 1200kg, find the force exerted by the engine. Relate this to Newton's Second Law.
Answer:
Case Summary

Car acceleration requires engine force.


Scientific Principle
  • F = ma (Newton's 2nd Law)
  • a = (v-u)/t

Solution Approach

a = (18-0)/6 = 3 m/s². F = 1200×3 = 3600N. Like NCERT's bus example, force depends on mass and acceleration.

Question 3:
Two ice skaters push each other. Skater A (60kg) moves at 2 m/s. If Skater B (40kg) moves backward, calculate her velocity using conservation of momentum.
Answer:
Case Summary

Skaters demonstrate action-reaction forces.


Scientific Principle
  • Total momentum before = after (Newton's 3rd Law)
  • m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Solution Approach

0 = 60×2 + 40×v → v = -3 m/s. Negative sign shows opposite direction, like the NCERT rocket example.

Question 4:
A bullet of mass 0.02kg strikes a wooden block at 200 m/s and stops in 0.1s. Calculate the retarding force and explain the effect on the block.
Answer:
Case Summary

Bullet impact demonstrates force and deceleration.


Scientific Principle
  • F = m(v-u)/t
  • Equal and opposite reaction affects the block

Solution Approach

F = 0.02(0-200)/0.1 = -40N (retarding). Block experiences 40N forward force, causing motion like NCERT's recoil examples.

Question 5:
A cricket ball of mass 150g is moving at 20 m/s. A batsman hits it back at 25 m/s. Calculate the change in momentum and identify the Newton's law applied here.
Answer:
Case Summary

A cricket ball's momentum changes after being hit.

Scientific Principle
  • Momentum (p) = mass × velocity
  • Newton's Third Law: Action-Reaction forces
Solution Approach

Initial momentum = 0.15kg × 20m/s = 3kg·m/s. Final momentum = 0.15kg × (-25m/s) = -3.75kg·m/s. Change = 6.75kg·m/s. The bat applies force (action), and the ball reacts (Newton's Third Law).

Question 6:
A car accelerates from rest to 10 m/s in 5 seconds. If its mass is 1000kg, find the force applied by the engine. Relate this to Newton's Second Law.
Answer:
Case Summary

A car accelerates due to engine force.

Scientific Principle
  • Force = mass × acceleration (F=ma)
  • NCERT example: Pushing a grocery cart
Solution Approach

Acceleration = (10m/s)/5s = 2m/s². Force = 1000kg × 2m/s² = 2000N. Like our textbook shows, greater mass requires more force for same acceleration (Newton's Second Law).

Question 7:
A bullet of mass 10g is fired from a gun. If the gun recoils at 1 m/s, calculate the bullet's velocity (gun mass=5kg). Name the conservation law used.
Answer:
Case Summary

A gun recoils after firing a bullet.

Scientific Principle
  • Law of Conservation of Momentum
  • Total momentum before = after
Solution Approach

0 = (0.01kg × v) + (5kg × -1m/s). Solving gives v=500m/s. Like in NCERT, momentum is conserved in isolated systems (e.g., rocket propulsion).

Question 8:
A book on a table doesn't move despite gravity. Identify forces and explain balanced forces using Newton's First Law.
Answer:
Case Summary

A stationary book has balanced forces.

Scientific Principle
  • Newton's First Law: Objects at rest stay at rest
  • NCERT example: Hanging lamp
Solution Approach

Gravity pulls down (weight), table pushes up (normal force). Since forces are equal and opposite, net force=0. As we studied, balanced forces cause no motion (Newton's First Law).

Question 9:
A car of mass 1000 kg moving at 20 m/s applies brakes and stops in 5 seconds. Case Summary: Calculate the retarding force and explain how Newton's Second Law applies here.
Answer:
Case Summary: A car decelerates due to braking force.
Scientific Principle: Newton's Second Law (F = ma).
Solution Approach:
  • Deceleration (a) = (v-u)/t = (0-20)/5 = -4 m/s²
  • Force (F) = ma = 1000 × (-4) = -4000 N (retarding force)

Our textbook shows similar problems with negative acceleration. Real-world example: Bicycle brakes reduce speed by friction.

Question 10:
A cricket ball of mass 150 g hits a bat at 10 m/s and returns at 5 m/s. Case Summary: Find the change in momentum and relate it to Newton's Third Law.
Answer:
Case Summary: Ball's momentum changes upon collision.
Scientific Principle: Momentum (p = mv) and action-reaction pairs.
Solution Approach:
  • Initial momentum = 0.15 × 10 = 1.5 kg m/s
  • Final momentum = 0.15 × (-5) = -0.75 kg m/s
  • Change = -0.75 - 1.5 = -2.25 kg m/s

NCERT example: A bouncing ball. Real-world: Tennis racket hitting a ball.

Question 11:
A rocket ejects gases at 2000 m/s, producing a thrust of 5000 N. Case Summary: Explain how Newton's Third Law causes motion and calculate the mass of gas ejected per second.
Answer:
Case Summary: Rocket propulsion via gas ejection.
Scientific Principle: Newton's Third Law (equal and opposite reaction).
Solution Approach:
  • Thrust = rate of momentum change = (mass/time) × velocity
  • 5000 = m × 2000 → m = 2.5 kg/s

Our textbook discusses rocket motion. Real-world example: Water rockets in school projects.

Question 12:
A book lies on a table. Case Summary: Identify the action-reaction pairs and forces acting on the book using Newton's Laws.
Answer:
Case Summary: Book at rest due to balanced forces.
Scientific Principle: Newton's First and Third Laws.
Solution Approach:
  • Action: Earth pulls book (weight = mg)
  • Reaction: Book pulls Earth (equal & opposite)
  • Table exerts normal force (N) = weight

NCERT example: A box on ground. Real-world: Laptop on desk.

Question 13:

A cyclist riding at a constant speed of 5 m/s applies brakes to stop the bicycle in 10 seconds. The mass of the cyclist along with the bicycle is 60 kg. Based on this information:

  • Calculate the retardation produced by the brakes.
  • Determine the force applied by the brakes to stop the bicycle.
Answer:

Retardation Calculation:
Initial velocity (u) = 5 m/s
Final velocity (v) = 0 m/s (since the bicycle stops)
Time taken (t) = 10 s

Using the equation of motion: v = u + at
0 = 5 + a × 10
a = -0.5 m/s² (negative sign indicates retardation)

Force Calculation:
Mass (m) = 60 kg
Retardation (a) = 0.5 m/s²

Using Newton’s Second Law: F = ma
F = 60 × 0.5 = 30 N

Additional Insight: The force applied by the brakes opposes the motion, hence the negative sign in acceleration. The magnitude of force (30 N) is sufficient to stop the bicycle within the given time.

Question 14:

Two friends, Riya and Priya, push a heavy box in the same direction. Riya applies a force of 40 N, while Priya applies 30 N. The box accelerates at 2 m/s². Answer the following:

  • Calculate the total force applied by both.
  • Determine the mass of the box.
Answer:

Total Force Calculation:
Force by Riya (F₁) = 40 N
Force by Priya (F₂) = 30 N

Since both forces act in the same direction, the total force (F) is:
F = F₁ + F₂ = 40 + 30 = 70 N

Mass Calculation:
Acceleration (a) = 2 m/s²
Total force (F) = 70 N

Using Newton’s Second Law: F = ma
70 = m × 2
m = 35 kg

Conceptual Note: The combined force leads to a higher acceleration compared to individual efforts. The mass (35 kg) is derived from the net force and observed acceleration, showcasing the direct relationship between force, mass, and motion.

Question 15:

A cyclist riding at a constant speed suddenly applies brakes, causing the bicycle to slow down and eventually stop. Using the concept of force and Newton's laws of motion, explain:

  • Why does the bicycle slow down when brakes are applied?
  • What role does friction play in this scenario?
Answer:

When the cyclist applies brakes, the brake pads press against the wheel rim, creating frictional force opposing the motion of the wheels. According to Newton's first law of motion, the bicycle tends to stay in motion due to inertia, but the frictional force acts as an unbalanced external force, causing deceleration.


Friction plays two key roles:

  • It converts the kinetic energy of the moving bicycle into heat energy, dissipating it.
  • It provides the necessary opposing force to stop the bicycle, as per Newton's second law (F = ma).

Without friction, the bicycle would not slow down, demonstrating its importance in controlling motion.

Question 16:

Two identical toy cars, A and B, are placed on a smooth table. Car A is pushed with a force of 5 N, and Car B is pushed with 10 N. Both cars start from rest.

  • Compare their accelerations using Newton's second law.
  • If Car B attains a velocity of 4 m/s in 2 seconds, calculate the mass of the toy cars.
Answer:

According to Newton's second law (F = ma), acceleration is directly proportional to the net force applied when mass is constant. Since Car B experiences double the force (10 N) compared to Car A (5 N), its acceleration will also be double.


To calculate the mass:


Given for Car B: F = 10 N, final velocity (v) = 4 m/s, time (t) = 2 s.


First, find acceleration (a):
a = (v - u)/t = (4 m/s - 0)/2 s = 2 m/s².


Now, using F = ma:
10 N = m × 2 m/s²
m = 10 N / 2 m/s² = 5 kg.


Thus, the mass of each toy car is 5 kg.

Question 17:

A cyclist is riding a bicycle at a constant speed of 5 m/s on a straight road. Suddenly, a dog runs onto the road 10 meters ahead. The cyclist applies brakes, causing a uniform deceleration of 2 m/s². Based on this scenario, answer the following:

  • Will the cyclist stop before hitting the dog? Show calculations.
  • State the law of motion that explains why the cyclist continues to move forward even after applying brakes.
Answer:

Step 1: Calculate stopping distance
Initial velocity (u) = 5 m/s
Deceleration (a) = -2 m/s²
Final velocity (v) = 0 m/s (since the cyclist stops)
Using the equation: v² = u² + 2as
0 = (5)² + 2(-2)s
0 = 25 - 4s
4s = 25
s = 6.25 m

Conclusion: The cyclist stops in 6.25 m, which is less than the 10 m distance to the dog. Hence, the cyclist will stop safely.

Law of motion involved: Newton's First Law of Motion (Inertia)
This law states that an object in motion stays in motion unless acted upon by an external force. The brakes provide the external force, but the cyclist's body tends to continue moving forward due to inertia.

Question 18:

Two friends, Riya and Priya, are pushing a heavy box in the same direction. Riya applies a force of 30 N, while Priya applies 20 N. The box experiences a frictional force of 10 N opposing the motion.

  • Calculate the net force acting on the box.
  • If the box has a mass of 10 kg, what will be its acceleration? (Use Newton's Second Law)
  • Explain why the box doesn't move if the applied forces are equal to the frictional force.
Answer:

Step 1: Calculate net force
Total applied force = Riya's force + Priya's force = 30 N + 20 N = 50 N
Frictional force (opposing) = 10 N
Net force = 50 N - 10 N = 40 N

Step 2: Calculate acceleration
Using Newton's Second Law (F = ma):
40 N = 10 kg × a
a = 40 N / 10 kg = 4 m/s²

Explanation for no motion: If applied forces equal frictional force (e.g., 10 N each), net force becomes zero. According to Newton's First Law, the box will remain at rest as there is no unbalanced force to change its state of motion.

Question 19:
A cricket player catches a fast-moving ball. He gradually pulls his hands backward while catching it.

(a) Why does he do this?
(b) Name the law involved in this scenario and explain it briefly.

Answer:

(a) The cricket player pulls his hands backward while catching the ball to increase the time of impact. This reduces the force exerted on his hands due to the impulse-momentum theorem (Force = Change in Momentum / Time). By increasing the time, the force decreases, preventing injury.

(b) The law involved is Newton's Second Law of Motion, which states that the rate of change of momentum of an object is directly proportional to the applied force and occurs in the direction of the force.
Mathematically, F = ma or F = Δp/Δt.
In this case, the player reduces the force by increasing the time (Δt), demonstrating the practical application of this law.

Question 20:
A car of mass 1000 kg moving at 20 m/s applies brakes and comes to rest in 5 seconds.

(a) Calculate the retardation of the car.
(b) Determine the force exerted by the brakes.

Answer:

(a) To find the retardation (negative acceleration), we use the formula:
a = (v - u) / t
where:
Final velocity (v) = 0 m/s (since the car comes to rest),
Initial velocity (u) = 20 m/s,
Time (t) = 5 s.

Substituting the values:
a = (0 - 20) / 5
a = -4 m/s² (The negative sign indicates retardation).

(b) The force exerted by the brakes is calculated using Newton's Second Law:
F = ma
where:
Mass (m) = 1000 kg,
Acceleration (a) = -4 m/s².

Substituting the values:
F = 1000 × (-4)
F = -4000 N (The negative sign indicates the force opposes motion).

Thus, the brakes exert a force of 4000 N in the opposite direction of motion to stop the car.

Question 21:
A cricket player catches a fast-moving ball. He gradually pulls his hands backward while catching it.

Based on this scenario, answer the following:

  • Explain the scientific principle behind this action.
  • How does this technique help in preventing injury?
Answer:

The cricket player pulls his hands backward while catching the ball to increase the time of impact, which reduces the force exerted on his hands. This is based on the Impulse-Momentum Theorem (F × t = Δp), where force is inversely proportional to time when momentum change is constant.


By increasing the time (t), the force (F) decreases, preventing injury. If he stops the ball abruptly, the high force could hurt his hands. This technique is also used in safety measures like airbags and cushioned seats.

Question 22:
Two identical toy cars, A and B, are moving at speeds of 2 m/s and 4 m/s, respectively. Both are brought to rest by applying the same braking force.

Answer the following:

  • Which car takes longer to stop? Justify your answer.
  • How does the stopping distance compare between the two cars?
Answer:

Car B (moving at 4 m/s) takes longer to stop because it has greater momentum (p = m × v). Since the braking force is the same, the time taken to stop depends on the initial momentum.


Stopping distance is directly related to kinetic energy (KE = ½ mv²). Since KE depends on v², Car B (with double the speed) has four times the KE of Car A. Thus, Car B requires a longer stopping distance to dissipate this energy.

Question 23:
A car of mass 1000 kg is moving with a velocity of 20 m/s. The driver applies the brakes, and the car comes to rest in 5 seconds. Calculate the force exerted by the brakes on the car. Also, explain how Newton's second law of motion is applied in this scenario.
Answer:

To calculate the force exerted by the brakes, we use Newton's second law of motion, which states that force (F) is equal to the product of mass (m) and acceleration (a), i.e., F = m × a.


First, we find the acceleration of the car. The car decelerates from 20 m/s to 0 m/s in 5 seconds.


Using the formula: a = (v - u) / t
where v = final velocity (0 m/s),
u = initial velocity (20 m/s),
t = time (5 s).


Substituting the values:
a = (0 - 20) / 5 = -4 m/s² (negative sign indicates deceleration).


Now, using F = m × a:
F = 1000 kg × (-4 m/s²) = -4000 N.


The negative sign indicates the force is opposing the motion, which is the braking force.


Application of Newton's second law: The law explains how the braking force causes the car to decelerate. The greater the mass or the required deceleration, the larger the force needed to stop the car.

Question 24:
Two objects, A and B, of masses 5 kg and 10 kg respectively, are moving with the same velocity. If the same force is applied to stop both objects, which one will come to rest first? Justify your answer using Newton's laws of motion.
Answer:

According to Newton's second law of motion, acceleration (a) is inversely proportional to mass (m) when the same force is applied, i.e., a = F / m.


Given:
Mass of object A = 5 kg,
Mass of object B = 10 kg,
Same force (F) is applied to both.


For object A:
aA = F / 5 kg.


For object B:
aB = F / 10 kg.


Since aA > aB, object A will decelerate faster and come to rest before object B.


Justification: The lighter object (A) has a higher deceleration for the same force, as per Newton's second law. Thus, it stops sooner. This also aligns with the concept of inertia (Newton's first law), where a larger mass (B) resists change in motion more than a smaller mass (A).

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