Q. 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) 2πa
B) A
C) $\frac{a}{2\pi}$
D) $\frac{a}{\pi}$
Explanation
(c) We have
$v^{2} = \rho gh$
$a^{2}\sqrt{\rho gh} = \pi r^{2}\ \sqrt{\rho gh} \times 2$
$r = \frac{a}{2\pi}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.