Question

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)`

Answer 1

Correct Answer - 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)`