Q. A tank is filled with water of density $1\ g\ {cm}^{- 3}$ and oil of density $0.9\ g\ {cm}^{- 3}$ . The height of water layer is 100 cm and of oil layer is 400 cm. If $g = 980\ {cm\ s}^{- 2}$ , then the velocity of efflux from an opening in the bottom of the tank is
A) $\sqrt{900 \times 980}\ {cms}^{- 1}$
B) $\sqrt{1000 \times 980}\ {cms}^{- 1}$
C) $\sqrt{920 \times 980}\ {cms}^{- 1}$
D) $\sqrt{950 \times 980}\ {cms}^{- 1}$
Explanation
(b) Let${\ d}_{w}$ and $d_{0}$ be the densities of water and oil, then the pressure at the bottom of the tank
$= h_{w}d_{w}g + h_{0}d_{0}g$
Let this pressure be equivalent to pressure due to water of height $h$ then
$hd_{w}g = h_{w}d_{w}g + h_{0}d_{0}g$
$\therefore\ h = h_{w} + \frac{h_{0}d_{0}}{d_{w}}$
$= 100 + \frac{400 \times 0.9}{1}$
$= 100 + 360 = 460$
According to Toricelli’s theorem,
$v = \sqrt{2gh} = \sqrt{2 \times 980 \times 460}$
$= \sqrt{920 \times 980\ }cm\ s^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.