Final answer:
The moment of inertia of a sphere of mass M and radius R about an axis passing through the centre is 2/5MR². The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is D. (√3/5)R.
Step-by-step explanation:
The moment of inertia of a sphere of mass M and radius R about an axis passing through the centre is 2/5MR². The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is D. (√3/5)R.
The radius of gyration, denoted by k, is a measure of how the mass of an object is distributed from its axis of rotation. For a sphere with a mass distribution along the entire radius, the radius of gyration is given by k = (√2/5)R.
Therefore, the correct answer is D. (√3/5)R.