Consider a cylindrical tank of radius $1 m$ is filled with water. The top surface of water is at $15\,m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5\,m$ from the bottom. A force of $5 \times 10^{5} N$ is applied an the top surface of water using a piston. The speed of efflux from the hole will be.
(given atmospheric pressure $P_{A}=1.01 \times 10^{5}\,Pa$, density of water $\rho_{ w }=1000\,kg / m ^{3}$ and gravitational acceleration $g=10\,m / s ^{2}$ )
JEE MAIN 2022, Diffcult
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Apply Bernoulli's theorem between Piston and hole $P_{A}+\rho g h=P_{0}+\frac{1}{2} \rho v_{e}^{2}$
Assuming there is no atmospheric pressure on piston
$\frac{5 \times 10^{5}}{\pi}+10^{3} \times 10 \times 10=1.01 \times 10^{5}+\frac{1}{2} \times 10^{3} \times v_{e}^{2}$
$v_{e}=17.8\,m / s$
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