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A thin uniform rod of length l and mass ...

A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is `omega`. Its cenre of mass rises to a maximum height of :

A

`(I omega)/( 6 g)`

B

`(l^(2)omega^(2))/(2g)`

C

`(l^(2)omega^(2))/(6g)`

D

`(l^(2)omega^(2))/(3 g)`

Text Solution

Verified by Experts

The correct Answer is:
C
If centre of mass rises to a maximum height h, then from loss in `K.E. =` gain in `P.E.`., we get
`(1)/(2)I omega^(2) = mgh`
`(1)/(2)((ml^(2))/(3))omega^(2) = mgh`
`h = (l^(2)omega^(2))/(6g)`
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