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Question

The acceleration of block A is a upwards and the acceleration of block C is f downwards. Find the acceleration of block B. Assume that the string is inextensible and all the pulleys are smooth and light.


A
12(fa), Upwards
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B
12(a+f), Downwards
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C
12(a+f), Upwards
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D
12(fa), Downwards
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Solution

The correct option is A 12(fa), Upwards


lA, lB and lC are the intercepts of the same string.
Since the string is inextensible,
lA+2lB+lC = constant
Double differentiating above equation w.r.t time t, we get equation in terms of acceleration,
aA2aB+aC=0
(Assuming increase in length as positive)
Since aA=a, aC=f
aB=fa2 (Upwards)

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