Velocity of Efflux (Torricelli) question from JEE Main 2014 (12 Apr, Shift 1)

Answer: (b)

1. Continuity: $-A\frac{dh}{dt} = \pi a^2\sqrt{2gh}$
2. Integrate from $h$ to 0: $t = \frac{A}{\pi a^2}\cdot\frac{2\sqrt{h}}{\sqrt{2g}} = \frac{A}{\pi a^2}\sqrt{\frac{2h}{g}}$
3. $t = \frac{\sqrt{2}A}{\pi a^2}\sqrt{\frac{h}{g}}$
4. So the answer is (b).