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=10m//s^(2))`.

Options

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

Answer

A

Explanation

Let `A ` = cross-section of tank
`a` = cross-section hole
`V` = velocity with which level decreases
`v` = velocity of efflux
(##A2Z_XI_C10_E01_207_S01##)
From equation of continuity `av = AV`
`implies V = (av)/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`
`P +rhogh+1/2rhoV^(2) = P+0+1/2rhov^(2)`
`v^(2)=(2gh)/(1-(a/A)^(2))`
`=(2xx10xx(3-0.525))/(1-(0.1)^(2)) = 50 (m//sec)^(2)`.