Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be `2MR^(2)//5`. Where M is the mass of the sphere and R is the radius of the sphere.

Explanation

Moment of inertia of sphere about any diameter = `(2)/(5)MR^(2)`
Applying theorem of parallel axes,
Moment of inertia of sphere about a tangent to the sphere = `(2)/(5)MR^(2)+M(R )^(2)`
`=(7)/(5)MR^(2)`.