Q 11-09-139JEE MainJEE Main 2019 (10 Jan, Shift 1)Easy
Water flows into a large tank with flat bottom at the rate of $10^{-4}\ \text{m}^3\text{s}^{-1}$. Water is also leaking out of a hole of area $1\ \text{cm}^2$ at its bottom. If the height of the water in the tank remains steady then this height is:
Answer: (A) $5.1\ \text{cm}$
Steady level: outflow $=$ inflow, so $A\sqrt{2gh} = 10^{-4}$.
$$\sqrt{2gh} = \frac{10^{-4}}{10^{-4}} = 1\ \text{m/s} \;\Rightarrow\; h = \frac{1}{2\times9.8} = 0.051\ \text{m} = 5.1\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics