A `U`-tube of length `L` contains liquid. It is mounted on a horizontal turn table rotating with an angular speed `omega` about one of its arms as shown in Fig Find the difference in heights (`h`) between the liquid columns in two vertical arms.

Options

A. `(omega^(2)L^(2))/(2sqrt(2)g)`
B. `(omega^(2)L^(2))/(2g)`
C. `(2omega^(2)L^(2))/g`
D. `(2sqrt(2)omega^(2)L^(2))/g`

Answer

B

Explanation

`dF=dmxomega^(2)`
and `(dp)=rhoomega^(2)int_(0)^Lomegadx`
`P_(2)-P_(1)=(rhoomega^(2)L^(2))/2`
or `impliesrhogH=(rhoomega^(2)L^(2))/2`
`H=(omega^(2)L^(2))/(2g)`