Question

A square hole of side length $l$ is made at a depth of $y$ and a circular hole is made at a depth of $4y$ from the surface of water in a water tank kept on a horizontal surface. If equal amount of water comes out of the vessel through the holes per second then the radius of the circular hole is equal to $(r,l<<y)$ :

• A. $l/\sqrt{2}$
• B. $l/2$
• C. $l/\sqrt{2\pi }$
• D. $\sqrt{2}\pi$

Answer 1

The correct option is C $l/\sqrt{2\pi }$

Given $A_1{v}_1=A_2{v}_2$

here $A_1=l^2\&A_2=\Pi r^2$

$v_1=\sqrt{2gh}{v}_2=\sqrt{2g4h}$

So $\sqrt{2gh}\times l^2=2\sqrt{2gh}\times \Pi r^2$

So $r=\frac{l}{\sqrt{2\Pi }}$