# Velocity of the liquid coming out of a small hole of u vessel containing two different liquids of density $2 \rho$ ans $\rho$ as shown is

$a)\;\sqrt {6gh}\\ b)\;2 \sqrt {gh} \\ c)\;2 \sqrt {2gh}\\ d)\;\sqrt {gh}$

Pressure at (1)
$P_1=P_{atm}+\rho g (2h)$
Applying Bernonli's Theorem between two point (1) and (2)
$P_{atm}+2 \rho gh+\rho g (2h)+\large\frac{1}{2}$$2 \rho v^2 \qquad= P_{atm}+(2 \rho)g (0)+\large\frac{1}{2}$$2 \rho v^2$
Solving we get,
$v= 2 \sqrt {gh}$
Hence b is the correct answer

edited Feb 18, 2014 by meena.p