Lesson 7 – Momentum & Collisions

Phase 1: IIT / JEE Solved Problems
Page 4 – Challenging Mixed Problems

Problems on this page demand strong algebra, clear physical reasoning, and proper use of restitution. These are typical of upper JEE Main / entry JEE Advanced.

                                                        

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Problem 1 (Elastic Collision – Ratio Type)

Two particles of masses 2 kg and 1 kg move along the same line with velocities 4 m/s and 1 m/s respectively. If the collision is elastic, find their velocities after collision.

Concept Used: Momentum + Energy conservation

Momentum before = 2×4 + 1×1 = 9

Elastic collision (e = 1):
v₂ − v₁ = u₁ − u₂ = 3

Solving equations:
v₁ = 2 m/s
v₂ = 5 m/s

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Problem 2 (Restitution Based)

A ball is dropped vertically on a smooth floor from a height h. If the coefficient of restitution between ball and floor is e, find the height to which the ball rises after first bounce.

Key Insight: Vertical collision → use speeds just before and after impact

Speed just before impact = √(2gh)

Speed after rebound = e√(2gh)

Height after rebound = e²h

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Problem 3 (Impulse + Variable Direction)

A particle moving with velocity 6 m/s strikes a wall at right angles and rebounds with velocity 4 m/s. Find the impulse imparted to the particle.

Concept Used: Impulse = change in momentum

Initial momentum = m×6
Final momentum = m×(−4)

Impulse = −4m − 6m = −10m

Magnitude of impulse = 10m N·s

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Problem 4 (Conceptual – Trick Question)

Can kinetic energy ever increase during a collision? If yes, give an example.

Answer:

Yes. In an explosion or collision involving internal energy release, kinetic energy can increase while momentum remains conserved.

Example: Explosion of a bomb at rest.

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🧠 IIT Strategy Notes (Page 4)

✔ Vertical collisions behave like 1-D collisions
✔ Heights after bounce depend on e² (VERY important)
✔ Impulse problems need careful sign handling
✔ Energy increase is possible only due to internal forces

👉 Next: Phase 1 – Page 5 (Final Phase-1 Wrap + Transition to Tough Problems)