Question

A ball of mass m is released from A inside a smooth wedge of mass m as shown in Fig. 8.269. What is the speed of the wedge when the ball reaches point B?

• A. $(\frac{gR}{3\sqrt{2}}{)}^{1/2}$
• B. $\sqrt{2gR}$
• C. $(\frac{gR}{2\sqrt{2}}{)}^{1/2}$
• D. $\sqrt{\frac{2}{3}gR}$

Answer 1

The correct option is A $(\frac{gR}{3\sqrt{2}}{)}^{1/2}$

$mgRsmJ=\frac{1}{2}m{u}^2+\frac{1}{2}m{v}^2$

$\Rightarrow v_{an}=0$

$\Rightarrow mu=mv$

$\Rightarrow u=v$

$\Rightarrow \frac{2gR}{\sqrt{2}}=u^2+v^2$

$\Rightarrow 2u^2=\frac{2gR}{\sqrt{2}}$

$\Rightarrow u=\sqrt{\frac{gR}{\sqrt{2}}}.$

Hence, the answer is $\sqrt{\frac{gR}{\sqrt{2}}}.$