A large cylindrical tank of cross-sectional area $1\ m^2 $ is filled with water. It has a small hole at a height of $1\ m $ from the bottom. $A$ movable piston of mass $5$ $kg$ is fitted on the top of the tank such that it can slide in the tank freely without friction. A load of $45$ $kg$ is applied on the top of water by piston, as shown in figure. The value of $v$ when piston is $7$ $m$ above the bottom is $(g = 10\ m/s^2)$ ....... $m/s$
Diffcult
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$\frac{1}{2} \rho v^{2}=\rho g h+\frac{M g}{A}$
$\Rightarrow \mathrm{v}=\sqrt{2 \mathrm{gh}+\frac{2 \mathrm{Mg}}{\rho \mathrm{A}}}=\sqrt{2 \times 10 \times 6+\frac{2 \times 50 \times 10}{10^{3} \times 1}}$
$=\sqrt{120+1}=\sqrt{121}=11 \mathrm{m} / \mathrm{s}$
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