Lesson 7 – Momentum & Collisions

Phase 2: IIT / JEE Tough Problems
Page 4 – Unequal Masses & Extreme Traps

This page contains problems where unequal masses, moving frames, and illusionary complexity confuse students. IIT expects you to see simplicity early.

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Problem 1 (Unequal Mass – Elastic)

A particle of mass m moving with velocity u collides elastically with another particle of mass 3m initially at rest. Find the velocities of both particles after collision.

IIT Strategy: Use standard elastic collision results

v₁ = (m − 3m)/(m + 3m) · u = −u/2

v₂ = (2m)/(m + 3m) · u = u/2

👉 Heavier mass moves slowly, lighter mass rebounds.

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Problem 2 (Moving Wall – Advanced)

A ball moving with velocity u strikes a wall moving away from it with velocity v. The collision is elastic. Find the velocity of the ball after collision.

Frame Trick:

In wall frame:
Relative velocity = u − v

Elastic collision → velocity reverses

Back to ground frame:
Final velocity = 2v − u

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Problem 3 (Looks Numerical – Is Conceptual)

Two particles collide such that after collision, both move with the same velocity. What type of collision is this?

Same final velocity → relative velocity after = 0
⇒ Coefficient of restitution e = 0

Collision is perfectly inelastic.

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Problem 4 (Hidden Energy Trap)

In a collision, momentum is conserved but kinetic energy increases. Is this possible? Explain.

Yes. Internal energy can convert into kinetic energy, as in explosions or compressed spring release.

👉 Momentum conservation ≠ energy conservation.

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Problem 5 (Extreme IIT Trap)

A bullet embeds into a block suspended by a string. Which quantity is conserved during collision?

✔ Momentum conserved (horizontal)
❌ Mechanical energy NOT conserved

👉 Very common IIT-JEE Advanced MCQ.

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🧠 IIT Advanced Thinking (Page 4)

✔ Unequal masses → expect rebound of lighter body
✔ Moving frames simplify ugly equations
✔ If final velocities are same → e = 0 instantly
✔ Momentum survives many situations energy doesn’t
✔ Read question twice before solving

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📌 Next Step

Next page includes:
✔ Multiple tricky MCQs
✔ Option elimination only
✔ “No-calculation” IIT questions

👉 Next: Phase 2 – Page 5