Q 11-09-101JEE MainJEE Main 2023 (1 Feb, Shift 2)Easy
The surface of water in a water tank of cross section area $750\ \text{cm}^2$ on the top of a house is $h$ m above the tap level. The speed of water coming out through the tap of cross section area $500\ \text{mm}^2$ is $30\ \text{cm s}^{-1}$. At that instant, $\dfrac{dh}{dt}$ is $x\times10^{-3}\ \text{m s}^{-1}$. The value of $x$ will be ______.
Numerical value type. Enter your answer.
Answer: 2
Continuity: $A_1\left|\dfrac{dh}{dt}\right|=A_2v$:
$$\left|\frac{dh}{dt}\right|=\frac{500\times10^{-6}\times0.3}{750\times10^{-4}}=2\times10^{-3}\ \text{m s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics