Question

A smooth sphere of mass \( M \) moving with velocity \( u \) directly collides elastically with another sphere of mass \( m \) at rest. After collision, their final velocities are \( V \) and \( v \) respectively. The value of \( v \) is

• A. \( \frac{2uM}{m} \)
• B. \( \frac{2uM}{M} \)
• C. \( \frac{2u}{1 + m/M} \)
• D. \( \frac{2u}{1 + M/m} \)

Hint:

In elastic collisions, the relative velocity of approach equals the relative velocity of separation.

Answer 1

The Correct Option is C

Step 1: Use conservation of momentum and energy for elastic collision.
In an elastic collision, both momentum and kinetic energy are conserved. Using the conservation equations, we can derive the final velocities after the collision.
Step 2: Derive the expression for \( v \).
Using the formulas for elastic collision in one dimension, we get the expression for the final velocity \( v \) of the second sphere as: \[ v = \frac{2u}{1 + m/M} \]
Final Answer: \[ \boxed{\frac{2u}{1 + m/M}} \]