Question

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ 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. $ \frac{L}{\sqrt{2\pi }} $
• B. $ 2\pi L $
• C. $ L $
• D. $ \frac{L}{2\pi } $

Answer 1

Answer: (A)

Velocity of efflux, $v=\sqrt{2 g h}$
where, $h$ denotes the depth of the hole.
The quantities of water flowing put per second from both holes are given to be the same
$A_{1}\, v_{1}=A_{2}\, v_{2} $
$(L)^{2} \sqrt{2 g y}=\left(\pi R^{2}\right) \sqrt{2 g(4 y)}$
$(L)^{2}=2 \pi R^{2} $
$R=\frac{L}{\sqrt{2 \pi}}$