Question

A thin, uniform metal rod of mass 'M' and length 'L' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is 'ω'. Its centre of mass rises to a maximum height of ______.

(g =acceleration due to gravity)

Options

• `(L^2omega^2)/(3g)`

• `(L^2omega^2)/g`

• `(L^2omega^2)/(2g)`

• `(L^2omega^2)/(6g)`

Answer 1

A thin, uniform metal rod of mass 'M' and length 'L' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is 'ω'. Its centre of mass rises to a maximum height of `underline((L^2omega^2)/(6g))`.

Explanation:

mgh `=1/2Iomega^2`

`I="mL"^2/3`

`therefore"mgh"=1/2("mL"^2/3)omega^2`

`"h"=1/(6g)L^2omega^2`