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two light identical springs of spring co...

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 :

A

`(1)/(2pi)sqrt((6k)/(m)`

B

`(1)/(2pi)sqrt((3k)/(m)`

C

`(1)/(2pi)sqrt((2k)/(m)`

D

`(1)/(2pi)sqrt(k)/(m)`

Text Solution

Verified by Experts

The correct Answer is:
A
For small oscillation
`2(k(l)/(2)theta)l//2=(ml^2)/(12)alpha`
`(kl^2 theta)/(2)=(ml^2)/(12)alpha`
`alpha=(6k)/(m)omega =sqrt((6k)/(m))`
`2 pi f = sqrt((6k)/(m))rArr f=(1)/(2pi)sqrt((6k)/(m))`.
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