First slide

Connected bodies

Question

The pulley arrangements shown in the figure are identical, the mass of the rope being negligible. In case (a) mass m is lifted by attaching a mass of 2 m to the other end of the rope. In case (b) the mass m is lifted by pulling the other end of the rope with a constant downward force F = 2 mg, where g is the acceleration due to gravity. The acceleration of mass m in case (a) is :

Moderate

A

zero
B

More than that in case (b)
C

Less than that in case (b)
D

Equal to that in case (b)

Solution

$Case (a) : a_{1} = \frac{2 mg - mg}{3 m} = \frac{g}{3}$
$Case (b) : a_{2} = \frac{2 mg - mg}{m} = g$

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