A uniform solid sphere has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?

The moment of inertia about central axis becomes 18 times to its original moment of inertia when its mass doubled and radius tripled, I₁ = 18I.

Explanation:

Moment of inertia of a uniform solid sphere about its central axis is given by the relation :

   ....(1)

Here I is moment of inertia, M is mass of the solid sphere and R is the radius of the solid sphere.

Now, the mass of the sphere becomes twice and radius becomes thrice i.e.

New mass of sphere = 2M

New radius of new sphere = 3R

The new moment of inertia is:

Substitute equation (1) in the above equation.