Question

A tank is filled with water of density $1\frac{g}{{cm}^3}$ and oil of density $0.9\frac{g}{{cm}^3}$. The height of water layer is $100cm$ and that of oil layer is 400 $cm$. If $g=980\frac{cm}{s^2}$, then the velocity of efflux from an opening in the bottom of the tank will be-

• (A) $(952.53)\frac{cm}{s}$
• (B) $(940.23)\frac{cm}{s}$
• (C) $(949.53)\frac{cm}{s}$
• (D) $(939.54)\frac{cm}{s}$

Answer 1

The Correct Option is C

Explanation:
Let $\mathrm{d}(\mathrm{w})$ and $\mathrm{d}(\mathrm{o})$ be densities of water and oil resp, then the pressure at the bottom of the tank will be$=\mathrm{h}(\mathrm{w})\times \mathrm{d}(\mathrm{w})\times \mathrm{g}+\mathrm{h}(\mathrm{o})\times \mathrm{d}(\mathrm{o})\times \mathrm{g}$Let this pressure be equivalent to pressure due to water of height h$\mathrm{h}\times \mathrm{d}(\mathrm{w})\times \mathrm{g}=\mathrm{h}(\mathrm{w})\times \mathrm{d}(\mathrm{w})\times \mathrm{g}+\mathrm{h}(\mathrm{o})\times \mathrm{d}(\mathrm{o})\times \mathrm{g}$$h=h(w)+[h(o)\times \frac{d(0)}{d(w)}]$$\mathrm{h}=100+[\frac{400(0.9)}{1}]$$\mathrm{h}=100+360=460\mathrm{cm}$According to Toricelli's theorem$v=\sqrt{2gh}v$$=\sqrt{2\times 980\times 460}v$$=\sqrt{920\times 980}v$$=\sqrt{901600}$Velocity of efflux $=949.53\frac{cm}{s}$Hence, the correct option is (C).