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A block ‘A’ of mass m is tied to a fixed point C on a horizontal table through a string passing
            round a massless smooth pulley B. A force F is applied by the experimenter to the pulley. Show
            that if the pulley is displaced by the distance x, the block will be displaced by 2x. The
            acceleration of the block and the pulley.

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$\frac{F}{m}, \frac{F}{4m}$

$\frac{F}{2m}, \frac{F}{m}$

$\frac{2F}{m}, \frac{F}{m}$

$\frac{F}{2m}, \frac{F}{4m}$

answer is A.

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Detailed Solution

$a c c e l e r a t i o n o f b l o c k (M) T = 2ma \Rightarrow a = \frac{T}{2m} f o r m, F - 2 T = ma = 0 \Rightarrow F = 2 T \Rightarrow T = F/2 ∴ a_{B} = \frac{F}{4m} (pulley)$

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