A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is `r` and angular velocity of rotation is `omega`, then the difference in the heights of the liquid at the centre of the vessel and the edge is.

Options

A. `(romega)/(2g)`
B. `(r^2omega^2)/(2g)`
C. `sqrt(2gromega)`
D. `(omega^2)/(2gr^2)`

Answer

B

Explanation

Balancing force on a particle of mass .dm. on the surface of liquid, at a distance x from the axis of rotation.
`dmomega^2xcos theta= "d"mgsin theta`
`tan theta=(omega^2x)/(g)`
`(dy)/(dx)=(omega^2x)/g`
`2yint_1^ydy=int_0^r(omega^2x)/g dx`
`y = (omega^2x^2)/(2g)=(omega^2r^2)/(2g)` Height