A cylindrical container filled with a liquid is being rotated about its central axis at a constant angular velocity `omega`. Four points A, B, C and D are chosen in the same plane such that ABCD is a square of side length a and AB is horizontal while BC is vertical. A and D lie on the axis of rotation. Let the pressure at A, B, C and D be denoted by `P_(A), P_(B), P_(C )` and `P_(D)`. Which of these options is correct ?

Options

A. `P_(C )gt P_(A)` for all values of `omega , P_(B)lt P_(D)` only if `omega gt sqrt((2g)/(a))`
B. `P_(C )gt P_(A)` and `P_(B)lt P_(D)` only if `omega gt sqrt((2g)/(a))`
C. `P_(C )gt P_(A)` for all values of `omega , P_(B)gt P_(D)` only is `omega gt sqrt((2g)/(a))`
D. `P_(C )gt P_(A)` and `P_(B)gt P_(D)` for all values of `omega`

Answer

C

Explanation

We know that `P_(B)=P_(A)+(1)/(2)rhoomega^(2)a^(2)`
`P_(D)=P_(A)+rhoga`
`P_(C)=P_(D)+(1)/(2)rhoomega^(2)a^(2)=P_(A)+rhoga+(1)/(2)rhoomega^(2)a^(2)`
Therefore, `P_(C)gtP_(A)` for all values of `omega and P_(B)gtP_(D)` only if `omegagtsqrt((2g)/(a))`