A liquid of density `'rho'` is rotated with an angular speed `'omega'` as shown in figure. Using the pressure equation concept find the equation of free surface of the liquid.
.

Explanation

Writing pressure equation along the path PMO.
`p_(P)+rho gy-(rho omega^(2)x^(2))/(2)=po`
Points `P`and `O `are open to atmosphere.
so, pressure at these point are same(= atmospheric pressure).Therefore, the above equation becomes,
`rho gy- (rho omega^(2)x^(2))/(2)=0` or,` y=((omega^(2))/(2g))(x^2)`
This is the required parabolic equation of free surface of liquid.