Lesson 7 – Momentum & Collisions

Phase 3: Exam Mastery
Page 10 – Objective 4 (Hard Numericals + Tricks)

This page contains difficult objective numericals inspired by IIT-JEE Main & Advanced. These questions test speed, sign discipline, and physical sense.

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Q1. (IIT-JEE)

A particle of mass 1 kg moving with velocity 10 m/s collides head-on elastically with a particle of mass 3 kg at rest. Find the speed of the first particle after collision.

Elastic collision formula:
v₁ = (m₁ − m₂)/(m₁ + m₂) · u₁

v₁ = (1 − 3)/(1 + 3) × 10 = −5 m/s

✔ Speed after collision = 5 m/s

Speed Trick: Lighter mass rebounds when hitting heavier mass.

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Q2. (JEE Main)

A ball is dropped from a height of 20 m. If the coefficient of restitution with the ground is 0.5, find the height reached after the first bounce.

Height after bounce = e²h

h₁ = (0.5)² × 20 = 5 m

✔ Height = 5 m

Memory Rule: Heights → e², Time → e

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Q3. (IIT-JEE Advanced)

Two identical particles move towards each other with speeds 6 m/s. After elastic collision, the speed of each particle becomes:

• A) 0
• B) 6 m/s
• C) 12 m/s
• D) Depends on mass

✔ Correct Answer: B

Concept: In COM frame, speeds remain same in elastic collision.

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Q4. (JEE Main)

A bullet of mass m strikes a block of mass M resting on a smooth surface and gets embedded. The speed of the block immediately after collision is:

Momentum conserved:
mu = (m + M)v

v = mu / (m + M)

✔ Correct expression obtained.

Trap: Do NOT use energy conservation.

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Q5. (IIT-JEE)

Two particles of masses m and 2m collide. If the coefficient of restitution is zero, which statement is correct?

• A) Both rebound
• B) Stick together
• C) KE conserved
• D) Momentum not conserved

✔ Correct Answer: B

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🧠 Speed & Accuracy Control (Objective 4)

✔ If masses are equal → expect symmetry
✔ If e = 0 → sticking, one equation only
✔ Negative velocity = direction change, not error
✔ Use standard elastic formulas when possible
✔ Avoid algebra explosion

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📌 Next

Next page will include:
✔ Mixed objective + reasoning
✔ Very high-trap questions
✔ Final objective practice before revision

👉 Next: Objective 5 (Page 11)