Question

Two balls A (mass M) and B (mass 2M) collide elastically. If A moves at 150 m/s and comes to rest, find velocity of B before collision. \( e = 1 \).

• A. \( 37.5\ \text{ms}^{-1} \)
• B. \( 12.5\ \text{ms}^{-1} \)
• C. \( 75\ \text{ms}^{-1} \)
• D. \( 25\ \text{ms}^{-1} \)

Hint:

Apply both conservation of momentum and coefficient of restitution in elastic collisions.

Answer 1

The Correct Option is A

Given elastic collision and A comes to rest: Use conservation of momentum: \[ M \cdot 150 + 2M \cdot (-v) = 0 \Rightarrow v = 75\ \text{m/s} \] From coefficient of restitution: \[ e = \frac{v_B - 0}{150 - (-v)} = 1 \Rightarrow v_B + v = 150 \Rightarrow v_B = 75 \Rightarrow v = 37.5\ \text{ms}^{-1} \]