• # question_answer A large open tank has two holes in its wall. One is a square hole of side a at a depth of $x$ from the top and the other is a circular hole of radius r at a depth $4x$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then r is equal to : A)  $2\pi a$                                   B)  a C)  $\frac{a}{2\pi }$                                  D)  $\frac{a}{\sqrt{2\pi }}$

Rate of flow $=\frac{d(Volume)}{dt}\,=Area\,\times \,$ (Velocity of flow) ${{v}^{2}}=2gh\Rightarrow \,{{a}^{2}}\,\sqrt{2gh}\,=\pi {{r}^{2}}\sqrt{2g\mu x}\times 2$ $\Rightarrow \,r=\frac{a}{\sqrt{2\pi }}$