Question

Equal volumes of two immiscible liquids of densities p and 2p are filled in a vessel as shown in the figure. Two small holes are punched 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 $\frac{v_1}{v_2}$ is

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

Answer 1

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

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

Now pressure at hole 2 is,

$P=h\rho g+\frac{h}{2}\times 2\rho g$

Applying Bernoulli's theorem,

$P_0+2h\rho g=P_0+\frac{1}{2}\left(2\rho \right)v_2^2$

where, $P_0=$ atmospheric pressure

$v_2=\sqrt{2gh}$

$\frac{v_1}{v_2}=\frac{\sqrt{2g\frac{h}{2}}}{\sqrt{2gh}}=\frac{1}{\sqrt{2}}$