Question

Tanks A and B open at the top contain two different liquids upto certain height in them. A hole is made on the wall of each tank at a depth 'h' from the surface of the liquid. The area of the hole in 'A' is twice that of in B. If the liquid mass flux through each hole is equal,then the ratio of the densities of the liquids respectively is:

• A. $\frac{2}{1}$
• B. $\frac{3}{2}$
• C. $\frac{2}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

Given area of $A=2$(Area of B)
Velocity of ejection for both $=\sqrt{2gh}$
Mass flux $=\rho AV$
Since given mass flux is same for both:
$\Rightarrow {\rho }_1{A}_{1}v={\rho }_2{A}_{2}v$
$\Rightarrow \frac{{\rho }_1}{{\rho }_2}=\frac{A_2}{A_1}=\frac{1}{2}$