Question

Equal volume of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in figure. Two small holes are made at depth $\frac{h}{2}$ and $\frac{3h}{2}$ from the surface of lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes, then $\frac{v_1}{v_2}$ will be

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}$

We have $v_1=\sqrt{2gh\left(h/2\right)}=\sqrt{gh}....\left(i\right)$
and by using Bernoulli's theorem
$\rho gh+2\rho g\left(\frac{h}{2}\right)=\frac{1}{2}\left(2\rho \right)v_2^2$
$\Rightarrow v_2=\sqrt{2}gh....\left(ii\right)$
From Eqs. (i) and (ii)
$\frac{v_1}{v_2}=\frac{1}{\sqrt{2}}$.