Question

Assuming the expression for the MI of a uniform solid sphere about its diameter, obtain the expression for its moment of inertia about a tangent.

Answer 1

Let M be the mass of a uniform solid sphere of radius R. Let I_CM be its MI about any diameter.

Then, I_CM = 2/5 MR².

Let I be its MI about a parallel axis, tangent to the sphere. Here, h = R = distance between the two axis.

By the theorem of parallel axis, I = I_CM + Mh²

= 2/5 MR² + MR² = 7/5 MR²