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The string in fig. is passing over small...

The string in fig. is passing over small smooth pulley rigidly attached to trolley A. If the speed of trolley is constant and qual to `v_(A)` towards right, speed and magnitude of acceleration of block B at the instant shown in figure are

A

`v_(B)=v_(A), a_(B)=0`

B

`a_(B)=0`

C

`v_(B)=3/5 v_(A)`

D

`a_(B)=(16v_(A)^(2))/(125)`

Text Solution

Verified by Experts

The correct Answer is:
C, D

`(y-h)+sqrt(x^(2)+h^(2))=l` or `(dy)/(dt)+(x)/(sqrt(x^(2)+h^(2))) (dx)/(dt) =0`
`(dy)/(dt)=-(x)/(sqrt(x^(2)+h^(2))) (dx)/(dt) implies (dy)/(dt)=-3/5 (-v_(A))`
`v_(B)=3/5 v_(A)`…(i)
`(d^(2)y)/(dt^(2)) = (v_(A)^(2)h^(2))/((x^(2)+h^(2))^(3//2)) implies a_(B)=v_(A)^(2) (16)/((5)^(3))=16/(125) v_(A)^(2)` ..(ii)
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