Two masses $m_{1}$ and $m_{2}$ are placed on a smooth horizontal surface and are connected by a string of negligible mass. A horizontal force $F$ is applied on the mass $m_{2}$ as shown in the figure. The tension in the string is

(\frac{m_{1}}{m_{1} + m_{2}}) F

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\frac{m_{2} F}{m_{1} + m_{2}}

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(\frac{m_{1}}{m_{2}}) F

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\frac{m_{2} F}{m_{1}}

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Solution

The correct option is A $(\frac{m_{1}}{m_{1} + m_{2}}) F$
Net external force acting on the system is $F$ .
Acceleration of the system $a = \frac{F}{m_{1} + m_{2}}$
Tension in the string $T = m_{1} a$
$⟹ T = \frac{m_{1}}{m_{1} + m_{2}} F$

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