A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed u.

The water going out will initially be less than the water flowing in. As a result, the water level will continue to rise. When the water level is h, the efflux velocity = $\sqrt{2\mathrm{gh}}.$ The level will stabilize when this reaches the inflow velocity since the filling tube's and the hole's cross sections have the same cross sectional area. Torricelli's theorem provides this height,

$\mathrm{v}=\sqrt{2\mathrm{gh}}$

$\frac{{\mathrm{v}}^2}{2\mathrm{g}}=\mathrm{h}$

Hence the correct answer is The water level will rise to a height v²/2g and then stop.