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)+"gt"))/((2M-mut))`
B. `(muV_(e))/((2M-mut))`
C. `(mu"gt")/((2M-mut))`
D. `(2muV_(e))/((2M-mut))`

Answer

A

Explanation

`Mg-T=M(dv)/(dt)`………(1)
`T+muv_(e)-(M-mut)g=(M-mut)(dV)/(dt)`……(2)
From (1) and (2) we get
`Mg+muV_(e)-(M-mut)g=(2M-mut)(dv)/(dt)`……….(3)
`(muv_(e)+mu"gt")=(2M-mut)(dv)/(dt)`…..(4)
`(dv)/(dt)=(mu(v_(e)+"gt"))/((2M-mut))`
`:.(dv)/(dt)=(mu(V_(e)+"gt"))/((2M-mut))`
so, correct answer is (A)