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A block of mass M and cylindrical tank w...

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.)

A

`(mu(V_(e)+"gt"))/((2M-mut))`

B

`(muV_(e))/((2M-mut))`

C

`(mu"gt")/((2M-mut))`

D

`(2muV_(e))/((2M-mut))`

Text Solution

Verified by Experts

The correct Answer is:
A
`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)
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