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Two masses of $1\, kg$ and $5\, kg$ are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in figure. The masses start moving during this interval; the reading of spring balance will be
More than $6\, kg$
Less than $6\, kg$
Equal to $6\, kg$
None of the above
Solution
Suppose $T$ be the tension in each part of the string passing over the pulley. $T$ is given by$:$
$T=\frac{2 m_{1} m_{2} g}{m_{1}+m_{2}}=\frac{2 \times 1 \times 5}{1+5} g=\frac{5}{3} g$
For equilibrium of the pulley there is an upward force of $2 T$ acting on the string joining the pulley to the spring. Therefore, reading of spring balance will be $2 T=g / 3 .$ So reading will be $10 / 3 k g$ which is less than $6 k g$
