A uniform rod AB of mass m and length L is tied, at its end B, to a thread which is attached to point P on the ceiling. Length of the thread PB is 0.75 L. The other end A of the rod is hinged at a point on the ceiling. Distance AP = 1.25 L. End B of the rod is pushed gently perpendicular to the plane of the figure and it starts oscillating
(a) Find the moment of inertia of the rod about line AP.
(b) Assuming that the triangle APB makes a small angle `theta` with the vertical plane, write the restoring torque acting on the rod.
(c ) Calculate the time period of small oscillations.

Answer

(a) `(3)/(25)mL^(2) " " (b) (3)/(10) mgL theta`
(c ) `2pi sqrt((2L)/(5g))`