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A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M = 7.01 kg and length L = 0.15 m that is pivoted freely about one end, with a solid sphere of the same mass, 7.01 kg, and a radius of L/2 centered about the free end of the rod.

a) What the moment of inertia of the pendulum about its pivot point?

b) What is the period of the pendulum for small oscillations?

c) Determine the length L that gives a period of T = 2.51 s.
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