A holiday ornament in the shape of a hollow sphere with mass 1.0×10 2 kg and rad

Question

A holiday ornament in the shape of a hollow sphere with mass 1.0×102 kg and radius 5.5×102 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum.

Calculate its period. (You can ignore friction at the pivot. The moment of inertia of the sphere about the pivot at the tree limb is 5MR2/3.)

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Explanation / Answer

I = (5/3)mr² = (5/3)*1*10-2*(5.5*10-2)2 = 50.417*10-6 kg-m2
T = 2(I/mgL) = 2**sqrt(5.042*10-5/(1*10-2*9.8*5.5*10-2)) = 0.608 sec.

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