two light identical springs of spring constant K are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. the rod is pivoted at its centre 'o' and can rotate freely in horizontal plane . The other ends of the two springs are fixed to rigid supportss as shown in figure . the rod is gently pushed through a small angle and released , the frequency of resulting oscillation is :

Options

A. `(1)/(2 pi) sqrt((2 k)/(M))`
B. `(1)/(2 pi) sqrt((k)/(M))`
C. `(1)/(2 pi) sqrt((6 k)/(M))`
D. `(1)/(2 pi) sqrt((24 k)/(M))`

Answer

C

Explanation

Restoring torque `=-2xx k((l)/(2) theta)(l)/(2)=(I d^(2) theta)/(dt^(2))`
`(d^(2) theta)/(dt^(2)) = ((kl^(2))/(2)(-theta))/((ml^(2))/(12))`
`rArr omega = sqrt((6k)/(M))`
`f = (omega)/(2pi) = (1)/(2 pi) sqrt((6k)/(m))`.