Question

Equal volume of two immiscible liquids of densities and $2 \rho$ are filled in a vessel as shown in figure. Two small holes are punched at depths $\frac{h}{2}$ and $\frac{3 h}{2}$ 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

Answer: (D)

$ v_{1}=\sqrt{2 g\left(\frac{h}{2}\right)}=\sqrt{g h}$
Using Bernoulli's theorem, we get
$P_{a}+\rho g h+2 \rho g\left(\frac{h}{2}\right)$
$=P_{a}+\frac{1}{2}(2 \rho) v_{2}^{2}$ or $v_{2}=\sqrt{2 g h}$
$\therefore \frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{2}}$