Conservation of Momentum Class 11 Notes, MCQs, Questions & Answers

 Conservation of Momentum Explained | Newton’s Laws, Collisions & Real-Life Examples

- Dr.Sanjaykumar Pawar 

Gun recoil and collision illustrate how total momentum remains conserved in an isolated system.

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Conservation of Momentum (NEET Level Notes)

1. Introduction

• The Law of Conservation of Momentum is based on Newton's Second Law and Newton's Third Law of Motion.
• It states that the total momentum of an isolated system remains constant if no external force acts on it.

Momentum: Momentum is the product of mass and velocity.

Momentum (p) = Mass × Velocity = mv

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2. Gun and Bullet Example

Statement:

A bullet is fired from a gun.

Explanation:

• Initially, both the gun and bullet are at rest.
• Therefore, their initial momentum is zero.

Initial Momentum = 0

Statement:

If the force on the bullet by the gun is F, then the force on the gun by the bullet is −F.

Explanation:

• According to Newton's Third Law:
• Every action has an equal and opposite reaction.
• The gun pushes the bullet forward with force F.
• The bullet pushes the gun backward with force −F.

Statement:

The two forces act for a common interval of time Δt.

• Both forces act for the same duration while the bullet is inside the barrel.

Statement:

According to Newton's Second Law, FΔt is the change in momentum of the bullet.

Impulse = Force × Time = FΔt

Impulse = Change in Momentum

FΔt = Δp

• The bullet gains forward momentum.

Statement:

−FΔt is the change in momentum of the gun.

• The gun gains momentum in the backward direction.

−FΔt = Δpg

Statement:

Since initially both are at rest, change in momentum equals final momentum.

pb = FΔt

pg = −FΔt

Where:

• pb = Momentum of bullet
• pg = Momentum of gun

Statement:

pg = −pb

• Gun and bullet have equal momentum.
• Directions are opposite.

pb + pg = 0

• Total momentum after firing remains zero.
• Therefore momentum is conserved.

Conclusion: The total momentum of the gun-bullet system remains constant.

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3. Isolated System

Definition: An isolated system is a system on which no external force acts.

Examples:

• Gun and bullet system
• Collision of two balls
• Explosion in outer space

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4. Why Total Momentum Remains Constant

• Internal forces may change the momentum of individual particles.
• However, these momentum changes occur in equal and opposite pairs.
• Therefore, the total momentum remains unchanged.

FAB = −FBA

ΔpA = −ΔpB

Net Change in Momentum = 0

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5. Law of Conservation of Momentum

Law: The total momentum of an isolated system of interacting particles remains constant.

Total Initial Momentum = Total Final Momentum

Pi = Pf

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6. Collision of Two Bodies

Consider two bodies A and B.

Before Collision:

• pA = Initial momentum of body A
• pB = Initial momentum of body B

After Collision:

• p'A = Final momentum of body A
• p'B = Final momentum of body B

Applying Newton's Second Law

FAB Δt = p'A − pA

FBA Δt = p'B − pB

These equations show that impulse equals change in momentum.

Applying Newton's Third Law

FAB = −FBA

Substituting:

p'A − pA = −(p'B − pB)

Rearranging:

p'A + p'B = pA + pB

This proves that total momentum before collision equals total momentum after collision.

pA + pB = p'A + p'B

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7. Elastic and Inelastic Collisions

A. Elastic Collision

• Momentum is conserved.
• Kinetic Energy is also conserved.

Pi = Pf

KEi = KEf

Examples:

• Billiard balls
• Gas molecules

B. Inelastic Collision

• Momentum is conserved.
• Kinetic Energy is not conserved.

Pi = Pf

KEi ≠ KEf

Some kinetic energy converts into:

• Heat
• Sound
• Deformation Energy

Examples:

• Car accident
• Clay sticking to a wall

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NEET Quick Revision Box

Law of Conservation of Momentum:
Total Initial Momentum = Total Final Momentum

For Two Bodies:
pA + pB = p'A + p'B

Gun-Bullet Relation:
pb = −pg

• Elastic Collision: Momentum ✔, Kinetic Energy ✔
• Inelastic Collision: Momentum ✔, Kinetic Energy ✘
• Isolated System: No external force acts.

Most Important NEET Fact:

Momentum is conserved in both elastic and inelastic collisions, provided no external force acts on the system.

Conservation of Momentum - Mind Map

CONSERVATION OF MOMENTUM
│
├── Based On
│   │
│   ├── Newton's Second Law
│   └── Newton's Third Law
│
├── Definition
│   │
│   └── Total momentum of an isolated system
│       remains constant if no external force acts
│
├── Momentum
│   │
│   ├── Symbol = p
│   ├── Formula = p = mv
│   └── Vector Quantity
│
├── Gun-Bullet Example
│   │
│   ├── Initially
│   │   ├── Gun at Rest
│   │   ├── Bullet at Rest
│   │   └── Total Momentum = 0
│   │
│   ├── Action-Reaction Forces
│   │   ├── Force on Bullet = F
│   │   └── Force on Gun = -F
│   │
│   ├── Impulse
│   │   ├── FΔt = Change in Bullet Momentum
│   │   └── -FΔt = Change in Gun Momentum
│   │
│   ├── Result
│   │   ├── pb = FΔt
│   │   ├── pg = -FΔt
│   │   ├── pg = -pb
│   │   └── pb + pg = 0
│   │
│   └── Conclusion
│       └── Momentum Conserved
│
├── Isolated System
│   │
│   ├── No External Force
│   ├── Only Internal Forces Act
│   └── Examples
│       ├── Gun-Bullet
│       ├── Collision
│       └── Explosion in Space
│
├── Why Momentum is Conserved?
│   │
│   ├── Internal Forces Occur in Pairs
│   ├── Equal and Opposite Forces
│   ├── FAB = -FBA
│   ├── ΔpA = -ΔpB
│   └── Net Change = 0
│
├── Law of Conservation
│   │
│   ├── Total Initial Momentum
│   │          =
│   ├── Total Final Momentum
│   │
│   └── Pi = Pf
│
├── Collision of Two Bodies
│   │
│   ├── Before Collision
│   │   ├── pA
│   │   └── pB
│   │
│   ├── After Collision
│   │   ├── p'A
│   │   └── p'B
│   │
│   ├── Using Newton's Laws
│   │   ├── FABΔt = p'A - pA
│   │   ├── FBAΔt = p'B - pB
│   │   └── FAB = -FBA
│   │
│   └── Final Equation
│       └── pA + pB = p'A + p'B
│
├── Types of Collision
│   │
│   ├── Elastic Collision
│   │   │
│   │   ├── Momentum Conserved
│   │   ├── Kinetic Energy Conserved
│   │   └── Examples
│   │       ├── Billiard Balls
│   │       └── Gas Molecules
│   │
│   └── Inelastic Collision
│       │
│       ├── Momentum Conserved
│       ├── Kinetic Energy Not Conserved
│       ├── Energy Changes Into
│       │   ├── Heat
│       │   ├── Sound
│       │   └── Deformation
│       │
│       └── Examples
│           ├── Car Accident
│           └── Clay Sticking to Wall
│
└── NEET Quick Facts
    │
    ├── Pi = Pf
    ├── pA + pB = p'A + p'B
    ├── pb = -pg
    ├── Elastic → KE Conserved
    ├── Inelastic → KE Not Conserved
    └── Momentum Conserved in Both
        (if no external force acts)

CBSE Class 11 Physics
Conservation of Momentum Question Bank

A. Multiple Choice Questions (MCQs)

1. The law of conservation of momentum is applicable when:

(a) External force acts on the system
(b) Internal forces are absent
(c) No external force acts on the system
(d) Kinetic energy remains constant

Answer: (c) No external force acts on the system

2. Momentum is conserved in:

(a) Elastic collisions only
(b) Inelastic collisions only
(c) Both elastic and inelastic collisions
(d) Neither

Answer: (c) Both elastic and inelastic collisions

3. SI unit of momentum is:

(a) kg m/s
(b) N
(c) J
(d) kg m²/s²

Answer: (a) kg m/s

4. A gun recoils after firing because:

(a) Conservation of energy
(b) Conservation of mass
(c) Conservation of momentum
(d) Newton's First Law

Answer: (c) Conservation of momentum

5. Momentum is a:

(a) Scalar quantity
(b) Vector quantity
(c) Dimensionless quantity
(d) Constant

Answer: (b) Vector quantity

B. Very Short Answer Questions (1 Mark)

1. Define momentum.

Answer: Momentum is the product of mass and velocity of a body.

2. State the law of conservation of momentum.

Answer: The total momentum of an isolated system remains constant.

3. What is an isolated system?

Answer: A system on which no external force acts.

4. Give one example of conservation of momentum.

Answer: Recoil of a gun.

5. Is momentum scalar or vector?

Answer: Vector quantity.

C. Short Answer Questions (2-3 Marks)

1. Why does a gun recoil after firing?

Initially, the gun and bullet are at rest, so total momentum is zero. After firing, the bullet gains forward momentum. To conserve momentum, the gun gains equal and opposite momentum and moves backward. This backward motion is called recoil.

2. Why is momentum conserved during collision?

During collision, the forces between the bodies are internal forces. These forces are equal and opposite according to Newton's Third Law. The momentum gained by one body equals the momentum lost by the other. Therefore total momentum remains constant.

3. Distinguish between elastic and inelastic collisions.

Elastic Collision	Inelastic Collision
Momentum conserved	Momentum conserved
Kinetic energy conserved	Kinetic energy not conserved
No deformation	Deformation may occur

D. Long Answer Questions (5 Marks)

1. State and prove the law of conservation of momentum.

Consider two bodies A and B. Initial momenta: pA and pB Final momenta: p'A and p'B According to Newton's Second Law: FABΔt = p'A − pA FBAΔt = p'B − pB According to Newton's Third Law: FAB = −FBA Therefore, p'A − pA = −(p'B − pB) Rearranging, pA + pB = p'A + p'B Thus total momentum before collision equals total momentum after collision. Hence the law of conservation of momentum is proved.

2. Explain conservation of momentum using the gun-bullet system.

Initially the gun and bullet are at rest. Initial momentum = 0 When the bullet is fired, it moves forward with momentum pb. The gun acquires equal and opposite momentum pg. Therefore, pb + pg = 0 Hence total momentum remains constant and momentum is conserved.

E. Assertion and Reason Questions

Assertion (A): Momentum is conserved during an inelastic collision.
Reason (R): No external force acts on the system.

Answer: Both Assertion and Reason are true and Reason is the correct explanation.

Assertion (A): Kinetic energy is conserved in all collisions.
Reason (R): Momentum is conserved in all collisions.

Answer: Assertion is false but Reason is true.

Assertion (A): A gun recoils backward after firing.
Reason (R): Momentum of gun and bullet are equal and opposite.

Answer: Both Assertion and Reason are true and Reason correctly explains the Assertion.

F. Fill in the Blanks

1. Momentum = ______ × velocity.

Answer: mass

2. SI unit of momentum is ______.

Answer: kg m/s

3. In an isolated system total ______ remains constant.

Answer: momentum

4. Gun recoil is due to conservation of ______.

Answer: momentum

5. Momentum is a ______ quantity.

Answer: vector

G. True or False

1. Momentum is conserved only in elastic collisions.

False

2. Momentum is a vector quantity.

True

3. Recoil of a gun is an example of momentum conservation.

True

4. Kinetic energy is conserved in all collisions.

False

5. An isolated system has no external force.

True

H. Case Study Questions

A gun of mass 5 kg fires a bullet of mass 0.02 kg. The bullet moves forward with high speed and the gun recoils backward.

1. Why does the gun recoil?

Answer: Due to conservation of momentum.

2. Which law explains equal and opposite forces?

Answer: Newton's Third Law.

3. What is the initial momentum before firing?

Answer: Zero.

4. Is momentum conserved?

Answer: Yes.

5. In which direction does the gun move?

Answer: Backward direction.

I. Statement Based Questions

Statement I: Momentum is conserved in both elastic and inelastic collisions.
Statement II: Kinetic energy is conserved only in elastic collisions.

Answer: Both statements are true.

Statement I: An isolated system experiences no external force.
Statement II: Total momentum remains constant in an isolated system.

Answer: Both statements are true.

J. Match the Columns

Column A	Column B
Momentum	kg m/s
Gun recoil	Conservation of momentum
Elastic collision	Kinetic energy conserved
Inelastic collision	Kinetic energy not conserved
Isolated system	No external force

Important CBSE Exam Questions

1. State and prove the law of conservation of momentum.
2. Explain recoil of a gun using conservation of momentum.
3. Differentiate between elastic and inelastic collisions.
4. Why is momentum conserved during collisions?
5. Explain isolated system with examples.
6. Derive pA + pB = p'A + p'B.
7. Explain the role of Newton's Third Law in conservation of momentum.