In the figure $m_{1} a n d m_{2} (< m_{1})$ are joined together by a pulley. When the mass $m_{1}$ is released from the height h above the floor, it strikes the floor with a speed:

\sqrt{2 g h (\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}

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\sqrt{2 g h}

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\sqrt{\frac{2 m_{2} g h}{m_{1} + m_{2}}}

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\sqrt{\frac{2 m_{1} g h}{m_{1} + m_{2}}}

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Solution

The correct option is A $\sqrt{2 g h (\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}$
Due to difference in masses across the pulley, the mass $m_{1}$ tends to move down with acceleration $a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} g$
From equation of motion,
$v^{2} - u^{2} = 2 a h$
$⟹ v^{2} - 0^{2} = 2 \frac{m_{1} - m_{2}}{m_{1} + m_{2}} g h$

$⟹ v = \sqrt{2 g h (\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}$

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