A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatoria

Question

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is

.2/5 MR^2

.2/3 MR^2

.5/7 MR^2

.7/5 MR^2

.3/2 MR^2

Answer 1

The moment of inertia about an axis through the centre of the sphere is 2mr^2 / 5.

Using the parallel axis theorem, the moment required is:

2mr^2 / 5 + mr^2

= 7mr^2 / 5.