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Newton's Laws for System of Particles

In the arrang...

Question

In the arrangement shown, the pulleys are fixed and ideal, the strings are light, $m_{1} > m_{2}$ and $S$ is a spring balance which is itself massless. The reading of $S$ (in units of mass) is

m_{1} - m_{2}

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

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

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

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Solution

The correct option is C $\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}$
The acceleration of the system $= (\frac{m_{1} + m_{2}}{m_{1} + m_{2}}) g$ and hence the tension $T$ in the string is $(\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}) g$ . The reading of the spring balance is $T$ (in units of force) and $\frac{T}{g}$ (in units of mass).

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