Lesson 7 – Momentum & Collisions

Phase 1: IIT / JEE Solved Problems
Page 3 – Multi-Concept Problems

This page focuses on IIT-style problems where momentum, impulse, energy, and restitution are used together. These problems test thinking depth.

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Problem 1 (Impulse + Collision)

A ball of mass 0.5 kg strikes a wall normally with velocity 12 m/s and rebounds with velocity 8 m/s. If the time of contact is 0.02 s, find the average force on the ball.

Concept Used: Impulse = Change in momentum

Initial momentum = 0.5 × 12 = 6 kg·m/s
Final momentum = 0.5 × (−8) = −4 kg·m/s

Change in momentum = −4 − 6 = −10 kg·m/s

Average force = Δp / Δt = −10 / 0.02 = −500 N

Magnitude of force = 500 N

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Problem 2 (Energy + Momentum)

Two identical balls collide elastically. One ball is moving with velocity u, the other is at rest. Prove that after collision, the moving ball comes to rest.

Concept Used: Momentum + Kinetic energy conservation

Let initial momentum = mu
Final momentum = mv₁ + mv₂

Using energy conservation and symmetry:
v₁ = 0, v₂ = u

👉 This is a classic IIT shortcut result.

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Problem 3 (Loss of KE – Advanced)

Two particles of masses m and 3m collide in one dimension. If the coefficient of restitution is 0.5, find the fraction of kinetic energy lost.

Concept Used: Loss of KE formula

Fraction of KE lost = (1 − e²) × (m₁m₂ / (m₁ + m₂)²)

= (1 − 0.25) × (3 / 16)
= 9 / 64

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Problem 4 (Explosion Concept)

A particle explodes into two fragments with equal masses. If one fragment moves with velocity v, find the speed of the other fragment.

Concept Used: Momentum conservation

Initial momentum = 0
mv₁ + mv₂ = 0

v₂ = −v₁

👉 Speeds are equal, directions opposite.

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🧠 IIT Thinking Strategy (Page 3)

✔ Think in vectors, not numbers
✔ Look for symmetry (equal masses, rest conditions)
✔ Energy equations give shortcuts in elastic collisions
✔ Explosion problems always start with zero momentum

👉 Next: Phase 1 – Page 4 (Challenging Mixed Problems)