Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s²)

Let A = cross-section of tank
a = cross-section hole 
V = velocity with which level decreases
v = velocity of efflux
 

From equation of continuity $\mathrm{av}=\mathrm{AV}\Rightarrow \mathrm{V}=\frac{\mathrm{av}}{\mathrm{A}}$    
By using Bernoulli's theorem for energy per unit volume 
Energy per unit volume at point A 
                           = Energy per unit volume at point B
$\mathrm{P}+\mathrm{\rho gh}+\frac{1}{2}{\mathrm{\rho V}}^2=\mathrm{P}+0+\frac{1}{2}{\mathrm{\rho v}}^2$

$\Rightarrow v^2=\frac{2gh}{1-{\left(\frac{a}{A}\right)}^2}=\frac{2\times 10\times (3-0.525)}{1-(0.1{)}^2}=50(m/sec{)}^2$