A uniform solid wooden sphere of mass m and radius r is spinning about an axis t

Question

A uniform solid wooden sphere of mass m and radius r is spinning about an axis through its center. In order to meet weight specifications, its mass needs to be increased without changing its size. This is done by adding a very thin uniform coating of a dense metal foil to the outer surface of the sphere. Such a coating will not appreciably change the diameter of the sphere. If you add enough of this foil to double the sphere's mass, what is the ratio of its new moment of inertia to the moment of inertia of the original wooden sphere without the foil?

Explanation / Answer

Initial mass = m    Radius = r

Initial moment of inertia = 2/5 mr2

After adding a metallic mass of m without changing the radius new moment of inertia = mr2 + 2/5 mr2

                                                                                                                              =7/5 mr2

Required ratio = (7/5) / (2/5) = 7 / 2

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