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 A ejecting water at speed v.(a)Water level will keep on rising in the tank. (b)No water can be stored in the tank. (c)Water level will rise to a height v^2/2g & then stop. (d) Water level will oscillate.
the water level will stop rising wen the rate of water coming from the tap is equal to rate of water falling from the hole...since their crosss sections are equal it will happen wen the velocities of water falling are equal...let it fill to a height h,then the velocity with which the water falls from the hole be v equal to that falling from the tap...then...hdg=0.5dv^2...using bernoullis equation...we get h=0.5v^2/g
Net rate of accumulation in the tank is (v-sqrt(2*g*h))*A. This will become zero at h = v^2/2g. So water level will rise upto this height and stop, So c is the right answer.
Moderation Team
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