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Question

# For the masses and ideal-massless pulleys shown in figure find the ratio of magnitudes of accelerations of masses A and B. Pulley C is fixed to the ceiling and pulley D is free to move vertically. All strings are inextensible and assume the string length to be equal between the pulley D and C and between the pulley D and the rigid support.

A
0.5
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B
5
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C
2
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D
0.2
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Solution

## The correct option is A 0.5 Since the string is inextensible, Length of string = constant Let xA and xB be the intercepts of the string, then xA+xA+xB=C ⇒2xA+xB=C Differentiating w.r.t time, we get ⇒|2VA|+|VB|=0 Again differentiating w.r.t time, we get ⇒|2aA|+|aB|=0 ⇒|aB|=2|aA| ∣∣∣aAaB∣∣∣=12=0.5

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