Find the time period of a simple pendulum if the mass of the bob is and mass of the rod is .
where is the moment of inertia about the axis of rotation
is the mass
is the distance of the centre of mass from the axis of rotation
The moment of inertia of a rod of mass , length about one end is , and the moment of inertia of the bob is , so
Total mass =
and, taking moments about the axis of rotation:
(I think you have some brackets missing in your answer!)