A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is `r` and the speed of revolution is `n` rotations/second, find the difference in height of the liquid at the centre of vessel and its sides.

Options

A. `h=(2pi^(2)n^(2)r^(2))/g`
B. `h=(4pi^(2)n^(2)r^(2))/g`
C. `h=(pi^(2)r^(2)n^(2))/g`
D. `h=(pi^(2)r^(2)n^(2))/g`

Answer

A

Explanation

When the cylindrical vessel rotats the velocity at the sides is higher. Hence pressure at the sides is lower.

Equation of sruface liquid is `y=(omega^(2)x^(2))/(2g)`
Here `omega=2pin`
`x=R`
`y=h`
`h=((2pin)^(2)(R^(2)))/(2g)=(2pi^(2)n^(2)r^(2))/g`