A particle of mass `m` is allowed to oscillate near the minimum of a vertical parabolic path having the equaiton `x^(2) =4ay`. The angular frequency of small oscillation is given by

Options

A. `sqrt(gh)`
B. `sqrt(2gh)`
C. `sqrt(((g)/(2a)))`
D. `sqrt(((g)/(a)))`

Answer

C

Explanation

`f =- mg sin theta` for small `'theta' sin theta = tan theta`
`f =- mg tan theta` here `tan theta = (dy)/(dx) = (2x)/(4a) = (x)/(2a)`
`f = - (mgx)/(2a) =- m omega^(2) x`