Lesson 7 – Momentum & Collisions

Phase 1: IIT / JEE Solved Problems
Page 2 – Moderate Level Problems

These problems require simultaneous use of momentum conservation, coefficient of restitution, and clear sign convention. They are typical of JEE Main (tough) and JEE Advanced (basic).

---

Problem 1

Two particles A and B of masses 2 kg and 4 kg move towards each other with speeds 6 m/s and 2 m/s respectively. If the coefficient of restitution is 0.5, find their velocities after collision.

Step 1: Choose direction

Take direction of A as positive.

Given:
m₁ = 2 kg, u₁ = +6 m/s
m₂ = 4 kg, u₂ = −2 m/s
e = 0.5

Momentum conservation:
2×6 + 4×(−2) = 2v₁ + 4v₂
12 − 8 = 2v₁ + 4v₂
2v₁ + 4v₂ = 4

Coefficient of restitution:
v₂ − v₁ = e(u₁ − u₂)
v₂ − v₁ = 0.5(6 − (−2)) = 4

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

---

Problem 2

A ball of mass 0.2 kg moving with velocity 10 m/s collides normally with a smooth wall and rebounds with velocity 8 m/s. Find the coefficient of restitution.

Concept Used: Relative velocity method

Relative velocity of approach = 10 m/s
Relative velocity of separation = 8 m/s

e = separation / approach = 8 / 10 = 0.8

---

Problem 3

Two bodies of masses 1 kg and 3 kg move in the same direction with velocities 8 m/s and 2 m/s respectively. Find the loss of kinetic energy if the coefficient of restitution is 0.5.

Concept Used: Loss of KE formula

Loss of KE = ½ × (m₁m₂ / (m₁ + m₂)) × (u₁ − u₂)² × (1 − e²)

= ½ × (3 / 4) × (6)² × (1 − 0.25)
= 10.125 J

---

Problem 4

A particle of mass m collides elastically with another particle of mass 2m initially at rest. Find the fraction of kinetic energy retained by the first particle after collision.

Key IIT Insight:

For elastic collision:
v₁ = (m − 2m)/(m + 2m) × u = −(1/3)u

Fraction of KE retained = (v₁² / u²) = (1/9)

---

📌 IIT / JEE Tips (Page 2)

✔ Fix sign convention before solving
✔ Use relative velocity directly when one body is wall
✔ Memorize loss of KE formula
✔ Fraction-type questions are common in JEE Advanced

👉 Next: Phase 1 – Page 3 (Multi-Concept IIT Problems)