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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))` |
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Answer» Correct Answer - 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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