Question

Equal volumes of two immisible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in figure. Two small holes are punched at depths $h/2$ and $3h/2$ 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. $1/2$
• C. $1/4$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (D)

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

$v_1=\sqrt{2g\left(\frac{h}{2}\right)}=\sqrt{gh}$ .......(i)
From Bernoulli's theorem
$\rho gh+2\rho g\left(\frac{h}{2}\right)=\frac{1}{2}\left(2\rho \right)v_2^2$
$\therefore v_2=\sqrt{2gh}$ .........(ii)
$\therefore \frac{v_1}{v_2}=\frac{1}{\sqrt{2}}$.