A block of mass `M` and cylindrical tank which contains water having small hole at bottom, which is closed initially (total mass of cylinder + water is also M), are attached at two ends of an ideal string which passes over an ideal pulley as shown. At `t = 0` hole is opened such that water starts coming out of the hole with a constant rate `mu kg//s` and constant velocity `V_(e)` relative to the cyliender. aSccleration of the block at any time `t` will be : (Given that string always remains taut.)

Options

A. `(mu(v_(e)+g t))/((2M-mut))`
B. `(muv_(e))/((2M-mut))`
C. `(mug t)/((2M-mut))`
D. none

Answer

A

Explanation

`Mg-T=M_(dv)/(dt)` ..(1)
`T+muv_(e)-(M_(0)-mut)g=(M_(0)-mut)(dV)/(dt)` ..(2)
From (1) and (2) we get
`Mg+muV_(e)-(M-mut)g=(2M-mut)(dv)/(dt)` ..(3)
`(muv_(e)+mug t)=(2M-mut)(dv)/(dt)` ..(4)
`(dv)/(dt)=(mu(v_(e)+g t))/((2M-mut))`