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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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