Compute all parts of following question given below:

Question: A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M and length L that is pivoted freely about one end, with a solid sphere of the same mass and a radius of L/4 attached to the free end of the rod.

Part A: Obtain an expression for the moment of inertia of the pendulum about its pivot point as a function of M and L.

Part B: Obtain an expression for the period of the pendulum for small oscillations as a function of M, L and g.

Part C: Determine the length L that gives a period of T = 1.51s.

Show all work, use additional paper if necessary.