Example 4.5 NCERT Solutions: Impulse and Reflection of Billiard Balls Explained

  NEET Physics: Impulse and Momentum Wall Collision Solved Step by Step

-Dr.Sanjaykumar Pawar 

Two identical billiard balls reflect from a rigid wall, demonstrating impulse, momentum change, and Newton's Third Law.

Internal Links

Related NCERT Examples

Plain text

Example 4.1 – Momentum of a Particle

Example 4.2 – Impulse and Force Relationship

Example 4.3 – Conservation of Momentum

Example 4.4 – Newton's Second Law Applications

Example 4.6 – Collision Problems

Related Physics Topics

Plain text

What is Momentum in Physics?

Impulse Formula and Numerical Problems

Newton's Laws of Motion Complete Notes

Conservation of Linear Momentum

Elastic and Inelastic Collisions

Projectile Motion Notes

Vector Resolution in Physics

Motion in Two Dimensions

NEET Mechanics Formula Sheet

Common NEET Physics Mistakes

Example 4.5 – Reflection of Two Billiard Balls from a Wall

Question

Two identical billiard balls strike a rigid wall with the same speed but at different angles. After collision, they are reflected without any loss of speed.

Find:

1. Direction of the force on the wall due to each ball.
2. Ratio of the magnitudes of impulses imparted to the balls by the wall.

Concepts Required

1. Momentum

Momentum = Mass × Velocity
p = mv

2. Impulse

Impulse = Change in Momentum
J = Δp = pf − pi

3. Newton's Third Law

If the wall exerts a force on the ball, then the ball exerts an equal and opposite force on the wall.

First find the force on the ball due to the wall, then reverse the direction to get the force on the wall.

Case (a): Ball Strikes Normally

Step 1: Initial Momentum

X-direction:

(px)initial = mu

Y-direction:

(py)initial = 0

Step 2: Final Momentum

After reflection, speed remains same but direction reverses.

(px)final = -mu

(py)final = 0

Step 3: Change in Momentum

Δpx = (-mu) - (mu)
Δpx = -2mu

Δpy = 0

Step 4: Impulse

Jx = -2mu
Jy = 0

Therefore impulse acts completely along the negative x-direction.

Step 5: Direction of Force

• Force on ball due to wall → Negative x-direction.
• Force is normal (perpendicular) to the wall.
• By Newton's Third Law, force on wall due to ball → Positive x-direction.

Case (b): Ball Strikes at 30°

Step 1: Initial Momentum Components

(px)initial = mu cos30°

(py)initial = -mu sin30°

Step 2: Final Momentum Components

After reflection:

• X-component changes sign.
• Y-component remains unchanged.

(px)final = -mu cos30°

(py)final = -mu sin30°

Why does only X-component change?

The wall can exert force only perpendicular (normal) to its surface. It cannot exert force parallel to the surface.

Therefore:

• X-component changes.
• Y-component remains same.

Step 3: Change in Momentum

Δpx = (-mu cos30°) - (mu cos30°)

Δpx = -2mu cos30°

Δpy = 0

Step 4: Impulse

Jx = -2mu cos30°

Jy = 0

Therefore impulse acts only along the negative x-direction.

Step 5: Direction of Force

• Force on ball due to wall → Negative x-direction.
• Normal to the wall.
• Force on wall due to ball → Positive x-direction.
• Also normal to the wall.

Answer to Part (i)

Case (a)

• Force on wall is normal to the wall.
• Direction is positive x-direction.

Case (b)

• Force on wall is also normal to the wall.
• Direction is positive x-direction.

Conclusion:

In both cases, force on the wall is perpendicular (normal) to the wall.

The force is NOT inclined at 30°.

Answer to Part (ii): Ratio of Impulses

Impulse in Case (a)

Ja = 2mu

Impulse in Case (b)

Jb = 2mu cos30°

Ratio

Ja / Jb = 2mu / (2mu cos30°)

Ja / Jb = 1 / cos30°

Since:

cos30° = √3 / 2

Ja / Jb = 2 / √3

≈ 1.15 ≈ 1.2

Final Answers

(i) Direction of Force on Wall

• Case (a): Normal to wall, positive x-direction.
• Case (b): Normal to wall, positive x-direction.

(ii) Ratio of Impulses

Ja : Jb
= 2mu : 2mu cos30°
= 1 : cos30°
= 2/√3 : 1

or

Ja/Jb = 2/√3 ≈ 1.15 ≈ 1.2

NEET Shortcut

• Parallel component of momentum remains unchanged.
• Perpendicular component reverses direction.
• Impulse depends only on perpendicular component.

Impulse = 2m(v⊥)

This shortcut can solve most NEET wall-collision questions within seconds.

Impulse Formula Explained with Cricket Ball Example for NEET

 Change in Momentum and Impulse Numerical Solution Step by Step

Example 4.4 – Impulse Imparted to a Cricket Ball (Easy NEET Notes)

Impulse imparted to a cricket ball when its direction reverses after being hit by a batsman.

- Dr.Sanjaykumar pawar 

Question

Example 4.4 A batsman hits back a ball

straight in the direction of the bowler without

changing its initial speed of 12 m s–1

.

If the mass of the ball is 0.15 kg, determine

the impulse imparted to the ball. (Assume

linear motion of the ball)

A batsman hits back a ball straight towards the bowler without changing its speed.

Given:

• Mass of ball, m = 0.15 kg
• Initial speed, u = 12 m/s
• Final speed, v = 12 m/s
• Direction changes completely after being hit.

Find the impulse imparted to the ball.

---

Step 1: Understand the Situation

Before hitting:

Bowler → Ball → Batsman

After hitting:

Bowler ← Ball ← Batsman

The ball returns in the opposite direction.

Important Concept

• Speed remains the same.
• Direction changes.
• Velocity changes because velocity depends on both speed and direction.

---

Step 2: Choose Positive Direction

Take the direction from batsman to bowler as positive (+).

Then:

• Initial velocity = −12 m/s (because ball is moving towards batsman)

• Final velocity = +12 m/s (because ball is moving towards bowler)

---

Step 3: Write Initial Momentum

Momentum = Mass × Velocity

Initial momentum:

pᵢ = m × u

pᵢ = 0.15 × (−12)

pᵢ = −1.8 kg m/s

---

Step 4: Write Final Momentum

Final momentum:

pᶠ = m × v

pᶠ = 0.15 × (+12)

pᶠ = +1.8 kg m/s

---

Step 5: Calculate Change in Momentum

Change in momentum:

Δp = pᶠ − pᵢ

Δp = (+1.8) − (−1.8)

Δp = 1.8 + 1.8

Δp = 3.6 kg m/s

---

Step 6: Use Impulse Formula

Impulse = Change in Momentum

Therefore,

Impulse = 3.6 N·s

(1 kg m/s = 1 N·s)

---

Final Answer

Impulse imparted to the ball = 3.6 N·s

Direction: From batsman towards bowler.

---

Quick NEET Shortcut

When an object rebounds with the same speed:

Initial momentum = −mv

Final momentum = +mv

Change in momentum:

Δp = (+mv) − (−mv)

Δp = 2mv

For this question:

Δp = 2 × 0.15 × 12

Δp = 3.6 N·s

✅ Answer = 3.6 N·s (towards the bowler)

---

NEET Exam Tip

Whenever a ball rebounds (comes back):

✔ Direction changes

✔ Use opposite signs for velocities

✔ Momentum change becomes large because:

Change in momentum = Final momentum − Initial momentum

and subtracting a negative number becomes addition.

INTERNAL LINK

• What is Momentum? Definition, Formula and Examples • Impulse and Momentum Relationship Explained • Newton's First Law of Motion Notes • Newton's Second Law of Motion Explained • Newton's Third Law of Motion Easy Notes • Law of Conservation of Momentum • Force and Acceleration Numericals • Important NEET Physics Formulas • Class 11 Mechanics Complete Notes • NEET Physics Chapter-Wise Questions

Impulse Class 11 Physics Notes | NEET & CBSE Complete Guide

Impulse and Momentum Class 11 | Definition, Formula, MCQs & Notes

Impulse explained using a cricket ball collision and force-time relation showing change in momentum.

- Dr.Sanjaykumar Pawar 

 IMPULSE

│

├── Introduction

│   │

│   ├── Large force may act for a very short time

│   ├── Such force can produce a noticeable change in momentum

│   └── This effect is studied using the concept of impulse

│

├── Example: Ball Hits a Wall

│   │

│   ├── Ball moves towards the wall

│   ├── Ball comes in contact with the wall

│   ├── Contact time is very short

│   ├── Wall exerts a large force on the ball

│   ├── Ball bounces back

│   └── Momentum changes direction

│

├── Need for Impulse

│   │

│   ├── Exact force is difficult to measure

│   ├── Exact contact time is difficult to measure

│   ├── Product of force and time can be measured

│   └── This product is called impulse

│

├── Definition of Impulse

│   │

│   ├── Impulse = Force × Time Duration

│   ├── Symbol: J

│   └── J = FΔt

│

├── Relation with Momentum

│   │

│   ├── Newton's Second Law

│   │   └── F = Δp/Δt

│   │

│   ├── Multiplying by Δt

│   │   └── FΔt = Δp

│   │

│   └── Therefore

│       └── Impulse = Change in Momentum

│

├── Formula

│   │

│   ├── J = FΔt

│   ├── J = Δp

│   └── J = pf − pi

│

├── SI Unit

│   │

│   ├── Newton-second (N·s)

│   ├── kg·m·s⁻¹

│   └── Same as momentum unit

│

├── Impulsive Force

│   │

│   ├── Very large force

│   ├── Acts for a very short duration

│   ├── Produces finite change in momentum

│   └── Called impulsive force

│

├── Characteristics of Impulsive Force

│   │

│   ├── High magnitude

│   ├── Short time interval

│   ├── Sudden action

│   └── Causes significant momentum change

│

├── Examples of Impulsive Force

│   │

│   ├── Bat hitting a cricket ball

│   ├── Football being kicked

│   ├── Hammer striking a nail

│   ├── Bullet hitting a target

│   └── Ball bouncing from a wall

│

├── Newtonian View

│   │

│   ├── Earlier treated separately

│   ├── Modern mechanics makes no distinction

│   ├── Impulsive force is an ordinary force

│   └── Difference:

│       ├── Very large magnitude

│       └── Very short duration

│

└── NEET Quick Revision

    │

    ├── Impulse = Force × Time

    ├── Impulse = Change in Momentum

    ├── J = FΔt = Δp

    ├── Unit = N·s

    ├── Impulsive force → Large force + Short time

    └── Key Examples:

        ├── Bat–Ball

        ├── Hammer–Nail

        ├── Bullet–Target

        └── Ball–Wall

Impulse (NEET Level Notes)

1. What is Impulse?

Sometimes a very large force acts on a body for a very short duration of time. Even though the time interval is small, the momentum of the body changes significantly. The effect produced by such a force is called Impulse.

Impulse is the product of force and the time interval for which it acts.

2. Example: Ball Striking a Wall

• Consider a ball moving towards a wall.
• When the ball hits the wall, contact lasts for a very short time.
• During this short interval, the wall exerts a large force on the ball.
• The ball bounces back in the opposite direction.
• Therefore, its momentum changes.

Although the force and contact time are difficult to measure separately, their product can be measured easily.

3. Definition of Impulse

Impulse = Force × Time Duration

J = FΔt

Where:

• J = Impulse
• F = Force
• Δt = Time interval

4. Relation Between Impulse and Momentum

According to Newton's Second Law of Motion:

F = Δp / Δt

Multiplying both sides by Δt:

FΔt = Δp

Therefore,

Impulse = Change in Momentum

J = Δp = pf − pi

Where:

• pf = Final Momentum
• pi = Initial Momentum

5. SI Unit of Impulse

Since:

Impulse = Force × Time

SI Unit:

Newton-second (N·s)

Since impulse equals change in momentum, it can also be written as:

kg·m/s

6. Impulsive Force

A large force acting for a very short time and producing a finite change in momentum is called an Impulsive Force.

7. Characteristics of Impulsive Force

• Very large magnitude.
• Acts for a very short duration.
• Produces a noticeable change in momentum.
• Can change speed, direction, or both.

8. Examples of Impulsive Forces

• Bat hitting a cricket ball.
• Football being kicked.
• Hammer striking a nail.
• Bullet hitting a target.
• Ball bouncing from a wall.

9. Important Concept

In earlier days, impulsive forces were treated as different from ordinary forces. However, according to Newtonian Mechanics, there is no special distinction.

An impulsive force is simply an ordinary force that is very large and acts for a very short interval of time.

NEET Quick Revision

• Impulse = Force × Time
• Impulse = Change in Momentum
• Formula: J = FΔt = Δp
• SI Unit: N·s or kg·m/s
• Impulsive Force: Large force acting for a short time.
• Examples: Bat-ball collision, hammer-nail, bullet-target, ball-wall collision.

NEET Definition: Impulse is the product of force and the time interval for which it acts, and it is equal to the change in momentum of the body.

CBSE Class 11 Physics – Impulse and Impulsive Force Question Bank with Answers

A. Multiple Choice Questions (MCQs)

1. Impulse is equal to:

a) Force × Velocity
b) Force × Time
c) Mass × Velocity
d) Work Done

Answer: (b) Force × Time

---

2. The SI unit of impulse is:

a) Newton
b) Joule
c) Newton-second
d) Watt

Answer: (c) Newton-second

---

3. Impulse is equal to:

a) Change in velocity
b) Change in force
c) Change in momentum
d) Change in acceleration

Answer: (c) Change in momentum

---

4. An impulsive force acts for:

a) Long duration
b) Infinite duration
c) Very short duration
d) Zero duration

Answer: (c) Very short duration

---

5. Which of the following is an example of impulsive force?

a) Gravitational force
b) Frictional force
c) Bat hitting a ball
d) Magnetic force

Answer: (c) Bat hitting a ball

---

6. If force doubles and time halves, impulse becomes:

a) Double
b) Half
c) Same
d) Zero

Answer: (c) Same

---

7. The dimension of impulse is:

a) [MLT^-1]
b) [ML²T^-2]
c) [MLT^-2]
d) [M⁰LT^-1]

Answer: (a) [MLT^-1]

---

8. Impulse-momentum theorem is based on:

a) Newton's First Law
b) Newton's Second Law
c) Newton's Third Law
d) Law of Gravitation

Answer: (b) Newton's Second Law

---

9. A force of 20 N acts for 5 s. Impulse is:

a) 4 Ns
b) 25 Ns
c) 100 Ns
d) 200 Ns

Answer: (c) 100 Ns

---

10. Impulse has the same unit as:

a) Energy
b) Work
c) Momentum
d) Power

Answer: (c) Momentum

B. Very Short Answer Questions (1 Mark)

1. Define impulse.

Answer: Impulse is the product of force and the time interval for which it acts.

2. Write the formula for impulse.

Answer: J = FΔt

3. State the SI unit of impulse.

Answer: Newton-second (N·s).

4. What is impulsive force?

Answer: A large force acting for a very short time is called an impulsive force.

5. What physical quantity does impulse change?

Answer: Momentum.

C. Short Answer Questions (2–3 Marks)

1. Show that impulse equals change in momentum.

Answer:
From Newton's second law,
F = Δp/Δt

Multiplying by Δt,
FΔt = Δp

Therefore,
Impulse = Change in Momentum

2. Why is a batsman allowed to move his hands backward while catching a ball?

Answer: Moving the hands backward increases the time of impact. Since impulse remains constant, force decreases. Therefore, the catch becomes easier and safer.

3. Give three examples of impulsive force.

Answer:

1. Bat striking a cricket ball.
2. Hammer striking a nail.
3. Bullet hitting a target.

4. Write any two characteristics of impulsive force.

Answer:

1. It has a very large magnitude.
2. It acts for a very short duration.

5. Why does a karate player break bricks with a quick blow?

Answer: The hand applies a large force for a very short duration, producing a large impulse that breaks the bricks.

D. Long Answer Questions (5 Marks)

1. Define impulse and derive the relation between impulse and momentum.

Answer:

Impulse is the product of force and the time interval during which it acts.

Impulse = Force × Time

According to Newton's Second Law,
F = Δp/Δt

Multiplying both sides by Δt,
FΔt = Δp

Therefore,
Impulse = Change in Momentum

J = FΔt = Δp

The SI unit of impulse is Newton-second (N·s).

2. Explain impulsive force with examples.

Answer:

An impulsive force is a large force acting for a very short duration producing a finite change in momentum.

Characteristics:

1. Large magnitude.
2. Short duration.
3. Produces considerable change in momentum.

Examples:

• Bat hitting a ball.
• Hammer striking a nail.
• Bullet striking a target.
• Ball rebounding from a wall.

E. Assertion and Reason Questions

1. Assertion (A): Impulse is equal to change in momentum.
Reason (R): Newton's second law leads to the relation FΔt = Δp.

Answer: Both A and R are true and R is the correct explanation of A.

2. Assertion (A): Impulsive force acts for a long time.
Reason (R): Impulsive force is very large in magnitude.

Answer: A is false but R is true.

3. Assertion (A): Impulse has the same unit as momentum.
Reason (R): Impulse equals change in momentum.

Answer: Both A and R are true and R correctly explains A.

4. Assertion (A): Catching a ball with rigid hands is safer.
Reason (R): Force decreases when contact time increases.

Answer: A is false but R is true.

F. Fill in the Blanks

1. Impulse is the product of Force and time.
2. Impulse is equal to change in Momentum.
3. SI unit of impulse is Newton-second.
4. A large force acting for a short time is called an Impulsive force.
5. Impulse and momentum have the same Unit.
6. Bat striking a ball is an example of Impulsive force.
7. Impulse is represented by the symbol J.
8. Impulsive force acts for a very Short duration.

G. Statement-Based Questions (True/False)

1. Impulse equals force divided by time. — False
2. Impulse equals force multiplied by time. — True
3. Momentum changes when impulse acts. — True
4. Impulsive force acts for a long duration. — False
5. Newton-second is the SI unit of impulse. — True
6. A hammer striking a nail is an example of impulsive force. — True
7. Impulse and work have the same unit. — False
8. Impulse can change the direction of motion. — True

H. Match the Following

Column A	Column B
1. Impulse	a. Change in momentum
2. N·s	b. Unit of impulse
3. Bat hitting ball	c. Impulsive force
4. FΔt	d. Impulse formula

Answers:
1 → a
2 → b
3 → c
4 → d

I. Case Study Questions

Case Study 1

A cricket player catches a fast-moving ball by moving his hands backward while catching it.

1. Why does the player move his hands backward?

Answer: To increase the time of impact.

2. What happens to the force when impact time increases?

Answer: Force decreases.

3. Which concept explains this phenomenon?

Answer: Impulse.

4. What remains constant during catching?

Answer: Change in momentum (Impulse).

Case Study 2

A hammer strikes a nail for a very short time and drives it into a wooden block.

1. What type of force acts on the nail?

Answer: Impulsive force.

2. Why is the force called impulsive?

Answer: It is very large and acts for a very short time.

3. What quantity changes due to impulse?

Answer: Momentum.

4. State the formula of impulse.

Answer: J = FΔt

Important CBSE Exam Definitions

Impulse:
The product of force and time interval during which it acts is called impulse.

Impulsive Force:
A large force acting for a very short duration producing a finite change in momentum is called an impulsive force.

Impulse-Momentum Theorem:
Impulse acting on a body is equal to the change in momentum of the body.