Question

A small ball $B$ of mass m is suspended with a light inelastic string of length $L$ from a block A of same mass m which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by the angle $\theta $ from equilibrium position & then released.

Maximum velocity of block during subsequent motion of the system after release of ball is

• A. $\left(\left[\textit{g} L \left(1 - \text{cos} \theta \right)\right]\right)^{1 / 2}$
• B. $\left(\left[2 \textit{g} L \left(1 - \text{cos} \theta \right)\right]\right)^{1 / 2}$
• C. $\left[\textit{g} L \text{cos} \theta \right]^{1 / 2}$
• D. Insufficient information to decide

Answer 1

Answer: (A)

KE gain by system = $mgL$ $\left(1 - \text{cos} \theta \right)$
half of that will be shared by block
$\frac{1}{2}\left(\textit{mv}\right)^{2}=\frac{1}{2}\textit{mg L}\left(1 - \text{cos} \theta \right)\Rightarrow \textit{v}=\sqrt{\textit{gL} \left(1 - \text{cos} \theta \right)}$