A holiday ornament in the shape of a hollow sphere with mass 1.0 Times 10^-2 kg

Question

A holiday ornament in the shape of a hollow sphere with mass 1.0 Times 10^-2 kg and radius 5.5 Times 10^*2 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 5MR^2/3.) Take the free fall acceleration to be 9.80 m/s^2. Express your answer using two significant figures.

Explanation / Answer

Given,

mass(m) = 1.0*10^-2 kg = 0.01 kg

radius(R) = 5.5*10^-2 m = 0.055 m

g = 9.8 m/s^2

T = [2*pi*sqrt(5*R)] / [sqrt(3*g)] = [2*3.14*sqrt(5*0.055)] / [sqrt(3*9.8)] = 3.293 / 5.422 = 0.607 s

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