First slide

Connected bodies

Question

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

Moderate

A

zero
B

more than that in case II
C

less than that in case II
D

equal to that in case II

Solution

$F = ma, a = g (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}), F - T = 0 and$
T = 2mg also T–mg = ma¹ Finally a < a¹

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