Lesson 7 – Momentum & Collisions

Phase 2: IIT / JEE Tough Problems
Page 1 – Advanced Thinking Level

This phase contains high-difficulty IIT/JEE problems where formulas alone will fail. Each problem is designed to expose hidden assumptions, traps, and conceptual gaps.

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Problem 1 (Hidden Frame Trap)

Two particles A and B of equal mass move towards each other with equal speeds u. They collide elastically. Find the velocities of the particles after collision.

Key IIT Insight:

System center-of-mass velocity = 0
Elastic collision in COM frame → velocities reverse

Final velocities = −u and +u

👉 Many students wrongly apply equations unnecessarily.

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Problem 2 (Multiple Collision Trap)

Three identical balls A, B, and C are placed in a straight line. A moves with velocity u and strikes B. All collisions are elastic. Find the final velocity of C.

IIT Shortcut:

Elastic collision + identical masses → velocity transfer

Velocity of C after all collisions = u

👉 Equivalent to Newton’s cradle.

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Problem 3 (Energy Increase Trap)

A shell at rest explodes into two fragments of equal mass. One fragment moves with velocity v. Find the kinetic energy of the system after explosion.

Concept: Momentum conserved, energy not conserved

Velocities = +v and −v

Total KE = 2 × (½ m v²) = m v²

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Problem 4 (Impulse Distribution)

A ball hits the ground vertically and rebounds. Which is greater: impulse during fall or rebound?

Correct Thinking:

Impulse during rebound is greater, because velocity changes from −u to +eu

👉 Many students answer incorrectly by intuition.

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⚠️ IIT-Level Traps Highlighted

❌ Solving in lab frame when COM frame is easier
❌ Writing equations blindly without symmetry check
❌ Forgetting sequence of multiple collisions
❌ Assuming KE is always conserved
❌ Trusting intuition instead of conservation laws

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📌 What’s Next?

Next page will include:
✔ Variable mass & moving frames
✔ Reverse-thinking problems
✔ Option-elimination strategies

👉 Next: Phase 2 – Page 2