Question

A tank is filled with water of density 1 g $c{m}^{-3}$ 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 cm $s^{-2}$, then the velocity of efflux from an opening in the bottom of the tank is :

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

Answer 1

Answer: (A)

$\sqrt{920\times 980}cm{s}^{-1}$

The pressure at the bottom of the tank must be equal to the pressure due to water of height h.

If $d_w$ and $d_o$ be the densities of water and oil respectively, then the pressure at the bottom of the tank

$=h_w{d}_{w}g+h_o{d}_{o}g$

If this pressure is equivalent to pressure due to water of height h.

Then,

$h{d}_{w}g=h_w{d}_{w}g+h_o{d}_{o}g$

$h=h_w+\frac{h_o{d}_o}{d_w}=100+\frac{400\times 0.9}{1}$

$=100+360=460$

According to Torricelli's theorem

$v=\sqrt{2gh}=\sqrt{2\times 980\times 460}$

$=\sqrt{920\times 980}cm{s}^{-1}$