The area of cross-section of a large tank… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022integermedium

The area of cross-section of a large tank is $0.5{m}^{2}$ . It has a narrow opening near the bottom having area of cross-section $1{\mathrm{cm}}^{2}$ . A load of $25\mathrm{kg}$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $40\mathrm{cm}$ above the bottom, will be _____ $\mathrm{cm}{s}^{-1}$ .

[Take $g=10{ms}^{-2}$ ]

Official previous-year question

Held on 27 Jun 2022 · Verified 6 Jul 2026.

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Solution

JEE Main 2022 Physics, Mechanical Properties of Fluids — solution figure

Pressure at point $1$ is ${P}_{1}={P}_{0}$ , Pressure at point $2$ is ${P}_{2}={P}_{0}+\frac{mg}{A}$

Applying Bernoulli's equation at top and bottom

${P}_{1}+\frac{1}{2}\rho {{v}_{1}}^{2}+\rho g{h}_{1}={P}_{2}+\frac{1}{2}\rho {{v}_{2}}^{2}+\rho g{h}_{2} \Rightarrow {P}_{0}+\frac{1}{2}\rho {v}^{2}+0={P}_{0}+\frac{mg}{A}+0+\rho gh$

$\Rightarrow \frac{250}{5}+{10}^{3}\times 10\times 0.4=\frac{1}{2}\times {10}^{3}\times {v}^{2}$

$v=3m{s}^{-1}=300\mathrm{cm}{s}^{-1}$

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