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Question

The string shown in the figure is passing over a smooth pulley rigidly attached to the trolley A. The speed of the trolley is constant and equal to vA. Speed and magnitude of acceleration of block B at the instant shown in the figure is vB and aB respectively, then

A
aB=6v2A125
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B
aB=16v2A125
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C
aB=16v2A25
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D
aB=24v2A125
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Solution

The correct option is B aB=16v2A125

(yh)+x2+h2=l
dydt+xx2+h2dxdt=0
dydt=xx2+h2dxdt
dydt=35vA
|vB|=35vA (i)
d2ydt2=[xx2+h2d2xdt2+dxdt(ddtxx2+h2)]

d2ydt2=[dxdt(ddtxx2+h2)]
(d2xdt2=aA=0)

d2ydt2=vA[(x2+h2)(dx/dt)(x2)(dx/dt)(x2+h2)3/2]

aB=⎢ ⎢ ⎢ ⎢v2Ah2(x2+h2)32⎥ ⎥ ⎥ ⎥

Since we are talking about magnitude of acceleration of B,
d2ydt2=v2Ah2(x2+h2)32
aB=v2A16(5)3
aB=16125v2A (ii)

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