Question

A slender uniform rod of mass `M` and length `l` is pivoted at one ens so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle `theta` with the vertical is

A. `(3g)/(2l)cos theta`
B. `(2g)/(3l)cos theta`
C. `(3g)/(2l)sin theta`
D. `(2g)/(3l)sin theta`

Answer 1

Correct Answer - C
As is clear from Fig.
torque about pivot `= 0, tau = I alpha`
`(mg sin theta)(l)/(2) = (ml^(2))/(3) alpha`
`alpha = (3g)/(2l)sin theta`