A smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

(m_{1} + m_{2}) g

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

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(m_{1} - m) g

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

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Solution

The correct option is B $\frac{(m_{1} - m_{2})^{2}}{m_{1} + m_{2}} g$
The equations of motion of the two blocks tied across a pulley are-
$m_{a} = m_{1} g - T$
and $m_{2} a = T - m_{2} g$
$⟹ a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} g$
Hence the net 'external' force acting on the blocks is
$m_{1} a - m_{2} a$
$= (m_{1} - m_{2}) a$
$= \frac{(m_{1} - m_{2})^{2}}{m_{1} + m_{2}} g$

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