A large cylindrical tank has a hole of area A at its bottom.Water is poured in the tank by a tuve of equal cross sectional area A ejecting water at a speed v. Which statement is true

a. The water level in the tank will keep on rising,

b. No water can be stored in the tank.

c. The water level will rise to a height v square/2g and then stop.

d. The water level will oscillate.

The answer for this question is c.

In the beginnig, the water is escaping the vessel with the rate of root(2gh)A (Toricelli equation) and filling it at the rate of vA.

So the rate of net change in water level of the vessel  at any instant is (v-root(2gh))A where h is the instataneous height.

Since h is quite small in the beginning, the water is escaping the vessel at a slow rate but filling at a much larger rate. as such (v-root(2gh))A is positive (increase in level of water)

Soon after the filling of water occurs, the height increases and rate of escape of water becomes larger 

But when rate of escape = rate of filling , then an equilibrium state is reached and there is no net change in the height of water.

This equlibrium is reached when (v-root(2gh))A=0 ----> h= v²/2g  

the water level will rise to a height vsquare\2g and than stop due to energy conservation principle

option (C)

water level comes down till the rate of inflow =rate of outflow.

i.e vel of water commin in and goin out must be equal

V = sqare root(2gH).