First slide

Connected bodies

Question

The system shown in the figure is released from rest. At the instant when mass M has fallen through a distance h, the velocity of m will be

Moderate

A

$\sqrt{2 g h}$
B

$\frac{\sqrt{2 g h M}}{m}$
C

$\sqrt{\frac{2 g h (M - m)}{m + M}}$
D

$\sqrt{\frac{2 g h (M + m)}{m - M}}$

Solution

$\begin{array}{l} loss in P.E. = gain in K.E. \\ (M - m) gh = \frac{1}{2} (M + m) v^{2} \\ ∴ v = \sqrt{\frac{2 gh (M - m)}{m + M}} \end{array}$

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