In the arrangement shown in the figure pulleys A and B are massless and the thread is inextensible. Mass of pulley C is equal to m. If friction in all the pulleys is negligible, then

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acceleration of pulley C is equal to g/2 (downward)

tension in thread is equal to (1/2) mg

acceleration of pulley A is equal to g (upward)

acceleration of pulley A is equal to 2g (upward)

answer is D.

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Detailed Solution

FBD of C

$m g - 2 T = m c$ ……(i)

If we assume acceleration of A to be 'a'
upwards; by constraint equation we get:

$- a - a + c + a + c = 0 \Rightarrow a = 2 c$

and for block A:

$2 T = m_{A} \cdot a but as m_{A} = 0 \Rightarrow T = 0$

$so we get c = g and a = 2 g ↑$

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