Lesson 7 – Momentum & Collisions

Stage 2: Board Exam Questions & Answers
Page 2 – Long Answer Questions

This section contains important long-answer questions frequently asked in Intermediate board examinations. Answers are written in a step-by-step, full-mark format.

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Q1. Derive the expression for conservation of linear momentum.

Answer:

Consider two bodies A and B of masses m₁ and m₂ moving along a straight line with velocities u₁ and u₂ before collision and v₁ and v₂ after collision.

According to Newton’s third law:

Force exerted by A on B = − Force exerted by B on A

Since force = rate of change of momentum:

Change in momentum of A = − Change in momentum of B

Hence:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

This proves the law of conservation of linear momentum.

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Q2. Explain elastic and inelastic collisions.

Answer:

Elastic Collision:

✔ Momentum conserved
✔ Kinetic energy conserved
✔ Coefficient of restitution e = 1

Inelastic Collision:

✔ Momentum conserved
❌ Kinetic energy not conserved
✔ 0 ≤ e < 1

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Q3. Explain recoil of a gun using conservation of momentum.

Answer:

Initially, the gun and bullet are at rest. Therefore, total momentum of the system is zero.

After firing:

Momentum of bullet + Momentum of gun = 0

Thus, the gun moves backward with a small velocity, which is called recoil.

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Q4. Derive expression for loss of kinetic energy in an inelastic collision.

Answer:

Loss of kinetic energy is given by:

Loss = ½ × (m₁m₂ / (m₁ + m₂)) × (u₁ − u₂)² × (1 − e²)

The loss depends on the coefficient of restitution and is maximum when e = 0.

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Q5. Explain two-dimensional collisions.

Answer:

In two-dimensional collisions, motion occurs in a plane.

✔ Momentum conserved along x-axis
✔ Momentum conserved along y-axis
✔ Vector analysis is required

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✔ Write derivations step-by-step
✔ Use proper equations and final result
✔ Draw neat diagrams if required

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