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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 centre of mass rises to a maximum height of -

A

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

B

`(1)/(6) (l omega)/(g)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`(1)/(2) I omega^(2) = mgh`
`(1)/(2) ((ml^(2))/(3) omega^(2)) = mgh`
`h = (omega^(2) l^(2))/(6 g)`.
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