Velocity of Efflux (Torricelli) question from JEE Main 2021 (27 Jul, Shift 1)

Answer: (c)

1. Efflux speed $v = \sqrt{2gh}$, so the jet's reaction force is $F = \rho a v^2 = 2\rho a g h$.
2. Vessel is light, so normal force = weight of liquid: $N = \rho A h g$.
3. No sliding: $\mu N \ge F \Rightarrow \mu \ge \frac{2\rho a g h}{\rho A h g} = \frac{2a}{A}$
4. So the answer is (c) $\frac{2a}{A}$.