Question

A tank is filled with water of density 1 g per $c{m}^3$ and oil of density 0.9 g $c{m}^{-3}$. The height of water layer is 100 cm and of the oil layer is 400 cm. If
g = 980 $c{m}^{-2}$ then the velocity of efflux from an opening in the bottom of the tank is

• A. $\sqrt{900\times 980}c{m}^{-1}$
• B. $\sqrt{1000\times 980}c{m}^{-1}$
• C. $\sqrt{92\times 980}c{m}^{-1}$
• D. $\sqrt{920\times 980}c{m}^{-1}$

Answer 1

The correct option is D $\sqrt{920\times 980}c{m}^{-1}$

Pressure at the bottom of tank must equal pressure due to water of height h
Let $d_w$ and $d_o$ be the densities of water and oil then the pressure at the bottom of the tank
$=h_w{d}_{w}g+h_o{d}_{o}g$

Let this pressure be equivalent to pressure due to water of height h
Then
$h{d}_{w}g=h_{w}g+h_o{d}_{o}g$
$h=h_w+\frac{h_o{d}_o}{d_w}$
$=100+\frac{400\times 0.9}{1}$
$=100+360$
$=460$
According to Toricelli's theorem
$v=\sqrt{2gh}$
$=\sqrt{2\times 980\times 460}$
$=\sqrt{920\times 980}$