The density of the earth is not quite uniform. It varies with the distance r from the

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The density of the earth is not quite uniform. It varies with the distance r from the center of the earth as r = C(1.22 - r/R), where R is the radius of the earth and C is a constant. 

(a) Find C in terms of the total mass M and the radius R. 

(b) Find the moment of inertia of the earth. (See Problem 40.)

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