A weightless rigid rod with a load at the end is hinged at point A to the wall so that it can rotate in all directions (Fig).

The rod is kept in the horizontal position by a vertical inextensible thread of length 1, fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure.
Determine the period T of small oscillations of the system.

Answer

B

Explanation

`T sin theta l = Ialpha`

`rArr -2mg thetal = m(4l^(3)) alpha rArr alpha = - (2g theta )/(4l)`
`rArr (d^(2) theta)/(dt^(2)) + (2g)/(4l) theta=0 rArr omega = sqrt((2g)/(4l)) = sqrt((g)/(2l)) rArr t = 2pisqrt((2l)/(g))`