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 given by

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

Hint:

In elastic collisions, both momentum and kinetic energy are conserved.

Answer 1

The Correct Option is C

Step 1: Use elastic collision formula.
For a one-dimensional elastic collision, the velocity of the second mass after collision is:
\[ V = \frac{2M}{M+m}\,u \]
Step 2: Rewrite expression.
\[ V = \frac{2u}{1 + \frac{m}{M}} \]
Step 3: Conclusion.
The correct expression for velocity \(V\) is \(\dfrac{2u}{1+\frac{m}{M}}\).