Lesson 7 – Momentum & Collisions

Phase 2: IIT / JEE Tough Problems
Page 3 – Chain Collisions & Hidden Constraints

This page contains true IIT-Advanced style problems where the difficulty lies in seeing the constraint, not in writing equations. These problems separate rankers from qualifiers.

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Problem 1 (Chain Collision – Conceptual)

Three identical balls A, B, and C are placed in a straight line on a smooth surface. Ball A moves with speed u and collides elastically with B. B then collides elastically with C. Find the final velocities of A, B, and C.

IIT Insight: Identical masses + elastic collisions

First collision (A with B):
A stops, B gets velocity u

Second collision (B with C):
B stops, C gets velocity u

Final velocities:
A = 0, B = 0, C = u

👉 This is the physics behind Newton’s cradle.

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Problem 2 (Hidden Constraint – No Numbers)

Two particles collide such that after collision, their velocities are perpendicular to each other. What can you say about the nature of collision?

IIT Reverse Thinking:

Perpendicular velocities after collision imply total kinetic energy is conserved.

Therefore, the collision is elastic.

👉 This result is often tested without calculations.

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Problem 3 (Variable Mass Thinking)

A body moving with velocity u breaks into two parts of masses m and 2m. The part of mass m moves with velocity v perpendicular to original direction. Find the velocity of the other part.

Key Idea: Momentum conserved in both directions

Initial momentum = 3m·u (along x-axis)

y-direction momentum must cancel → second fragment has y-component −(mv)

x-direction momentum of second fragment = 3mu

👉 Velocity is obtained using vector momentum balance.

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Problem 4 (Conceptual Trap – External Force)

A man jumps from a moving boat onto the shore. Is momentum conserved for the man-boat system?

❌ Momentum is NOT conserved
External force from water/ground acts during jump

👉 System boundary must be chosen carefully.

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🧠 IIT-Advanced Level Learning (Page 3)

✔ Chain collisions can be solved mentally
✔ Numbers may not be needed — reasoning is enough
✔ Momentum must be conserved component-wise
✔ External force destroys momentum conservation
✔ Visualize before solving

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📌 Next Step

Next page will cover:
✔ Multi-collision with unequal masses
✔ Advanced option-elimination problems
✔ Questions that look impossible but are simple

👉 Next: Phase 2 – Page 4