Lesson 7 – Momentum & Collisions

Phase 2: IIT / JEE Tough Problems
Page 2 – Moving Frames & Reverse Thinking

This page trains the student to change reference frames, think backward from answers, and eliminate options without full calculation — the exact skills used by IIT toppers.

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Problem 1 (Moving Reference Frame)

A ball A of mass m moving with velocity u collides elastically with another identical ball B moving with velocity v in the same direction. Find the velocities after collision.

IIT Strategy: Shift to frame moving with ball B

In B’s frame:
Velocity of A = (u − v)
Velocity of B = 0

Elastic collision + equal masses → velocity exchange

Transforming back to ground frame:
v₁ = v
v₂ = u

👉 Velocities exchange — without algebra.

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Problem 2 (Reverse Thinking Trap)

After a one-dimensional collision, two particles are observed to move with equal speeds in opposite directions. What can be said about the collision?

Reverse Logic:

Equal and opposite velocities → COM velocity = 0

Possible cases:
✔ Equal masses, elastic collision
✔ Explosion from rest

👉 Question tests interpretation, not calculation.

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Problem 3 (Impulse + Frame Shift)

A particle moving with velocity u collides with a wall moving towards it with velocity v. Find the velocity of the particle after collision if the collision is elastic.

IIT Frame Trick:

Move to wall’s frame:
Initial relative velocity = u + v

Elastic collision → velocity reverses

Transform back:
Final velocity = −u − 2v

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Problem 4 (Option Elimination – IIT Style)

In which case is momentum NOT conserved?

• A) Explosion in space
• B) Collision of two skaters on ice
• C) Bullet fired from a gun
• D) Ball colliding with the Earth

Correct Answer: D
External force from Earth acts on the ball alone

👉 System definition matters.

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🧠 IIT Advanced Thinking Skills (Page 2)

✔ Switch frames when algebra looks messy
✔ Think backward from final motion
✔ Define the system clearly before conservation
✔ Use elimination in MCQs instead of full solving
✔ Read what is asked — not what you expect

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📌 Next Step

Next page includes:
✔ Variable mass systems
✔ Chain collisions
✔ Hidden constraint problems

👉 Next: Phase 2 – Page 3