Question

Equal volume of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $\frac{h}{2}$ 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 $v_1/v_2$ is

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

Answer 1

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

$V_1=\sqrt{2g\frac{h}{2}}=\sqrt{gh}$

for $V_2$, applying bernaulis theorem

$P_0+O+O=P_0+\frac{1}{2}{\left(2\rho \right)V}_2^2-(\rho gh+2\rho g\frac{h}{2})$

$\Rightarrow V_2^2=2gh$

$\Rightarrow V_2=\sqrt{2gh}$

$\Rightarrow$ $\frac{V_1}{V_2}=\frac{1}{\sqrt{2}}$