JEE Mains · Physics · STD 11 - Fluid mechanics
- JEE Mains 2022
- Hard
- MCQ
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 \(g=10\,m / s ^{2}\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(17.8\)
Step-by-step Solution
Detailed explanation
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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