Question

A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth 'y' 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

Answer 1

$\begin{array}{c}\pi R^2\sqrt{2gy}=l^2\sqrt{8gy}\\ \Rightarrow \pi R^2=2l^2\\ \Rightarrow R=\frac{\sqrt{2}l}{\sqrt{\pi }}\end{array}$.