Lesson 7 – Momentum & Collisions

Phase 1: IIT / JEE Solved Problems
Page 1 – Basic to Moderate Level

This section introduces IIT / JEE style problems that test conceptual clarity + application. Each problem is solved step-by-step with exam-oriented reasoning.

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Problem 1 (JEE Main Level)

A particle of mass 1 kg moving with velocity 10 m/s collides head-on elastically with a stationary particle of mass 3 kg. Find the velocity of the 1 kg particle after collision.

Concept Used: Conservation of momentum + e = 1

Momentum equation:
1×10 + 3×0 = 1v₁ + 3v₂ → 10 = v₁ + 3v₂

Coefficient of restitution (e = 1):
v₂ − v₁ = 10

Solving the equations:
v₁ = −5 m/s

👉 Negative sign indicates reversal of direction.

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Problem 2 (JEE Main Level)

Two particles of equal masses collide elastically. One particle is initially at rest. What will be their velocities after collision?

Key IIT Insight:

In elastic collision of equal masses:
✔ Velocities are exchanged

👉 Moving particle comes to rest and stationary particle moves with the initial velocity of the first particle.

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Problem 3 (JEE Main Level)

A ball of mass 0.5 kg strikes a wall normally with speed 20 m/s and rebounds with the same speed. Calculate the impulse imparted to the ball.

Concept Used: Impulse = Change in momentum

Initial momentum = 0.5 × 20 = 10 kg·m/s
Final momentum = 0.5 × (−20) = −10 kg·m/s

Impulse = −10 − 10 = −20 N·s

Magnitude of impulse = 20 N·s

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Problem 4 (JEE Main Level)

A shell at rest explodes into two fragments of masses 4 kg and 1 kg. The lighter fragment moves with velocity 20 m/s. Find the velocity of the heavier fragment.

Concept Used: Momentum conservation in explosion

4v + 1×20 = 0

v = −5 m/s

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📌 IIT / JEE Exam Tips (Page 1)

✔ Always apply momentum conservation first
✔ Use e equation only after momentum equation
✔ Look for symmetry (equal masses, rest conditions)
✔ Sign convention decides direction

👉 Next: Phase 1 – Page 2 (Moderate IIT Problems with Mixed Concepts)