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. $\frac{2u}{1+\frac{m}{M}}$
• D. $\frac{2u}{1+\frac{M}{m}}$

Answer 1

The correct option is C $\frac{2u}{1+\frac{m}{M}}$

Using Newton's law of collision,

$\frac{V-v}{u-0}=-e$

$\frac{V-v}{u-0}=-1$ $⟹V=v-u$ $(\because e=1)$

Applying conservation of momentum just before and after the collision :

$Mu+0=MV+mv$

$Mu=M(v-u)+mv$

$⟹v=\frac{2Mu}{M+m}$

OR $v=\frac{2u}{1+\frac{m}{M}}$