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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-mu t))`B. `(muV_(e))/((2M-mu t))`C. `(mu "gt")/((2M-mu t))`D. `(2muV_(e))/((2M-mu t))` |
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Answer» Correct Answer - A A block of ………….. `Mg - T = M (dv)/(dt)` ……… (1) `T+mu V_(e)-(M-mu t)g = (M-mu t) (dV)/(dt)` ……. (2) From (1) and (2), we get `Mg+mu V_(e)-(M-mu t)g = (2M-mu t)(dv)/(dt)` …. (3) `(mu V_(e)+mu gt) = (2M-mu t) (dv)/(dt)` ……(4) `(dv)/(dt) = (mu (V_(e)+gt))/((2M-mu t))` `:. (dv)/(dt) = (mu(V_(e)+gt))/((2M-mu t))` So, correct answer is `(A)` |
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