Two masses $m_{1}$ and $m_{2}$ are connected by light inextensible string passing over a smooth pulley. $P$ . If the pulley moves vertically upwards with an acceleration equal to $g$ then.

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The acceleration of mass $m_{1}$ with respect to ground is $\frac{3 m_{2} - m_{1}}{m_{1} + m_{2}} g$

The acceleration of mass $m_{1}$ with respect to ground is $\frac{2 (m_{2} - m_{1})}{m_{1} + m_{2}} g$

Tension on the string is $\frac{2 m_{1} m_{2} g}{m_{1} + m_{2}}$

Tension on the string is $\frac{4 m_{1} m_{2} g}{m_{1} + m_{2}}$

answer is A, D.

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Detailed Solution

$Relative to the centre of the pulley, pseudo forces m_{1} g and m_{2} g are acting on masses m_{1} and m_{2} respectively . T = \frac{4 m_{1} m_{2} g}{m_{1} + m_{2}} a_{Pulley Centre} = \frac{2 (m_{2} - m_{1}) g}{m_{1} + m_{2}} \Rightarrow a_{ground} = \frac{3 m_{2} - m_{1}}{m_{1} + m_{2}} g$