Q 11-09-112JEE MainJEE Main 2021 (27 Jul, Shift 1)Medium
A light cylindrical vessel is kept on a horizontal surface. Area of the base is $A$. A hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is
Answer: (C) $\dfrac{2a}{A}$
Let the liquid height be $h$. Efflux speed $v = \sqrt{2gh}$.
Thrust of the jet on the vessel: $F = \rho a v^2 = 2\rho a g h$.
The vessel is light, so its weight is that of the liquid: $W = \rho A h g$; maximum friction $= \mu\rho A h g$.
$$\mu \rho A h g \ge 2\rho a g h \Rightarrow \mu_{\min} = \frac{2a}{A}$$
Solution by Sreeraj P, M.Sc Physics