What is filled in a cylindrical container to a height of `3 m`. 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//s^2)`.

Options

A. `50 m^2//s^2`
B. `50.5 m^2//s^2`
C. `51 m^2//s^2`
D. `52 m^2//s^2`

Answer

A

Explanation

Let `A` = cross-sectional of tank
`a` = cross-section hole
`V` = velocity with which level decreases
`v` = velocity of efflux
From equation of continuity, `av = AV`
`rArr V = (av)/(A)`
By using Bernoullis therom for energy per unit volume.
Energy per unit volume at point `A` = energy per unit volume at point `B`.
`p + rho gh + (1)/(2) rho v^2 = p + 0 + (1)/(2) rho v^2`
`rArr v^2 = (2 gh)/(1 - ((a)/(A))^2) =(2 xx 10 xx(3 - 0.525))/(1 -(0.1)^2)`
=`50 (m//s)^2`.