Question

Equal volume of two immiscible liquids of densities r and 2r are filled in a vessel as shown in 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 $\frac{v_1}{v_2}$ 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 $\frac{1}{\sqrt{2}}$


$v_1=\sqrt{2g\times \frac{h}{2}}$
Since density is different, apply Bernoulli theorem for $v_2$
Since holes are open to atmosphere Pressure = $P_{\circ }$ (atmosphere)
$P_{\circ }+\rho gh+2\rho g\frac{h}{2}=P_{\circ }+\frac{1}{2}2\rho v_2^2$
$v_2=\sqrt{2gh}\frac{v_1}{v_2}=\frac{1}{\sqrt{2}}$