A smooth horizontal disc rotates about the vertical axis `O` (figure) with a constant angular velocity `omega`. A thin uniform rod `AB` of length `l` performs small oscillation about the vertical axis `A` fixed to the disc at a distance `a` from the axis of the disc. Find the frequency `omega_(0)` of these oscillations.

Options

A. `sqrt((3a)/(2l)) omega`
B. `sqrt((a)/(l)) omega`
C. `sqrt((3a)/(l)) omega`
D. `sqrt((3a)/(l)) omega`

Answer

A

Explanation

Problem can be solved in rotatory frame. In disturbed condition:

From diagram:
`(a)/(sinr) = (r)/(sin(pi-theta)) rArr r = (a sin theta)/(sin r) ……….(1)`
`:.` torque about `A` is `tau =- mr omega^(2) ((l)/(2)sin theta_(1)) ........(2)`
`tau = I alpha = (ml^(2))/(3) alpha ........(3) theta` is small.
Solve for angular frequency, `omega_(0) = ? `