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

Answer 1

Answer: (C)

$V_{2 f}=\left(\frac{m_{2}-m_{1}}{m_{1}+m_{2}}\right) u_{2}+\left(\frac{2 m_{1}}{m_{1}+m_{2}}\right) u_{1}$
Here $u_{1}=u, u_{2}=0, m_{1}=M, m_{2}=m, V_{2 f}=v$
$\Rightarrow v=\left(\frac{2 M}{M+m}\right) u$
$\Rightarrow v=\frac{2 u}{1+\frac{m}{M}}$