• # question_answer A rectangular tank is filled to the brim with water. When a hole at its bottom is unplugged, the tank is emptied in time T. If the tank is half-filled with water, it will be emptied in time A) $\frac{T}{\sqrt{2}}$                         B) $\frac{T}{\sqrt{3}}$             C)      $\frac{T}{2}$           D)      $\frac{T}{2\sqrt{2}}$

The velocity of efflux through a hole is given by $v=\sqrt{2gh}.$If the hole is at the top of the tank, v is obviously zero. Therefore, the average velocity of efflux ${{V}_{a}}=\frac{1}{2}\sqrt{2gh}=\sqrt{\frac{gh}{2}}.$ If the volume of water in the tank when it is full, is V and A the cross sectional area of the hole, then the time taken by the taken to the emptied is $T=\frac{V}{A{{v}_{a}}}=\frac{\sqrt{2}V}{A\sqrt{gh}}$ when the tank is half-full, V is replaced by $\frac{v}{2}\And \,h$is replaced by$h/2.$ Therefore, the time taken is mow $T'=\frac{\sqrt{2}V/2}{A\sqrt{gh}/2}=\frac{V}{A\sqrt{gh}}=\frac{T}{\sqrt{2}}$ Hence, the correction option is (a).