Consider a parabola `y=Ax^(2)+B, -x_(0) le x le x_(0)`.

If this curve is rotated about y axis, we get a paraboloid surface. The volume below this surface & above x–z plane is given by `V=(piAx_(0)^(4))/2+piBx_(0)^(2)=("volume of cylinder ABCD")/2+"Volume of cylinder CDEF"`
Use the above result to answer following question.
If the cylinder of previous problem was completely filled, then the minimum angular velocity at which base may be visible is.

Options

A. `sqrt((gh)/(a^(2)))`
B. `sqrt((2gh)/(a^(2)))`
C. `sqrt((gh)/(2a^(2)))`
D. `sqrt(4/3(gh)/(a^(2)))`

Explanation

`y=(omega^(2)x^(2))/(2g)`
`h=(omega^(2)a^(2))/(2g)`
`omega=sqrt((2gh)/(a^(2)))`