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

Options

A. `V_(B)=V_(A),a_(B)=0`
B. `V_(B)=(3)/(7)V_(A)`
C. `a_(B)=(16)/(25)V_(A)^(2)`
D. `a_(B)=(16)/(125)V_(A)^(2)`

Answer

D

Explanation

`(y-4)+sqrt(x^(2)+(4)^(2))=l`
`(dy)/(dt)+(x)/(sqrt(x^(2)+16))(dx)/(dt)=0`
`(dy)/(dt)=-(3)/(5)V_(A)=V_(B)`
`(d^(2)y)/(dt^(2))=V_(A)(16)/((x^(2)+16)^((3)/(2)))`
`a_(B)=(16)/(125)V_(A)^(2)`