Question

A small ball of mass $m$ is released from rest from the position shown. All contact surfaces are smooth. The speed of the ball when it reaches its lowest position is

• A. $\sqrt{\frac{2 \, g \, R}{3}}$
• B. $\sqrt{\frac{4 \, g \, R}{3}}$
• C. $\sqrt{g \, R}$
• D. $\sqrt{2 \, g \, R}$

Answer 1

Answer: (B)

Let the speed of ball be $v$ and speed of the wedge be $v_{2 m}$
using conservation of momentum
$0=mv+2mv_{2 m}$
$v_{2 m}=-\frac{v}{2}$
Now, using work-energy theorem on the system,
$mgR=\frac{1}{2}\left(mv\right)^{2}+\frac{1}{2}\left(\right.2m\left.\right)\times \left(\frac{v}{2}\right)^{2}$
$\Rightarrow \, v=\sqrt{\frac{4 gR}{3}}$