Question

Water is being poured in a vessel at a constant rate $\alpha \, m^{3} \, s^{- 1}$ . There is a small hole of the area $a$ at the bottom of the tank. The maximum level of water in the vessel is

• A. $h=\frac{\alpha ^{2}}{2 g a^{2}}$
• B. $h=\frac{\alpha ^{2}}{4 g a^{2}}$
• C. $h=\frac{\alpha ^{2}}{ g a^{2}}$
• D. $h=\frac{3 \alpha ^{2}}{g a^{2}}$

Answer 1

Answer: (A)

Level of water in the vessel will be maximum when $rate \, of \, inflow \, of \, water=rate \, of \, outflow \, of \, water$ .
or $\alpha =av$

or $\alpha =a\sqrt{2 g h}$
or $h=\frac{\alpha ^{2}}{2 g a^{2}}$