A large cylindrical tank has a hole of area A at its bottom and water is poured into the tank through a tube of cross-sectional area ‘A’ ejective water at the speed ‘V’. Which statement of the following is true?

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Water level will rise to a height $\frac{v^{2}}{2 g}$ and then stop

The water level will be oscillating

Water level in tank keeps on rising

No water can be stored in the tank

answer is A.

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Detailed Solution

Initially, the water flowing out will be less than that flowing into it. Hence, the water level will go on rising when the water level is ‘h’ the velocity of efflux is $\sqrt{2 g h}$ , when this becomes equal to the velocity of inflow, the level will become steady as the area of cross section of the filling tube and area of cross section of the hole are equal. This height is given by torricelli’s theorem,
$V = \sqrt{2 g h} (o r) h = \frac{v^{2}}{2 g}$
There after the water level will not rise.