Question

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.

(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 v²/2 g and then stop. 

(d) The water level will oscillate.

Answer 1

(c) The water level will rise to a height v²/2 g and then stop.

EXPLANATION: 

Initially, the velocity of the water coming out of the tank will be negligible due to the negligible height of the water. So the quantity of the water coming out of the tank per second is less than the coming in, so the level of the water in the tank will begin to rise and the velocity of the water coming out will begin to increase. The level of the water will rise up to a height h for which the velocity of the water coming out is equal to the velocity of the water coming in (= v). So, v =√(2gh)  

→h =v²/2g.