The moment of inertia of a rigid hemisphere about diameter of a base is (a) $Ma^2/5$ (b) $Ma^2/2$ (c) $2Ma^2/5$ (d) More information needed

Question

While solving question,

The moment of inertia of a rigid hemisphere of mass $M$ and radius $a$ about a diameter of a base is

(a) $Ma^2/5$ (b) $Ma^2/2$ (c) $2Ma^2/5$ (d) More information needed ?

I know that moment of inertia of rigid sphere of mass $M$ and radius $a$ about a diameter of a base is $2Ma^2/5,$ So, I guess that

It should be same for hemisphere because now $M$ is mass of hemisphere not total mass of sphere? Am I right? Thanks

Answer 1

If the axis of rotation is the symmetry axis (from center of base, orthogonal to the tip of the hemisphere), then I = 2/5 m a² .

So your assumption is right. Best regards