Answer:
moment of inertia of sphere 2 is 32 times the moment of inertia of sphere 1
Explanation:
The moment of inertia of a solid sphere about its axis is
where
M is the mass of the sphere
R is the radius of the sphere
The mass of the sphere can be rewritten as
where
is the density
is the volume of the sphere
So the moment of inertia becomes
Calling R the radius of sphere 1, the moment of inertia of sphere 1 is
where is the density of steel, since the sphere is made of steel
Sphere 2 has twice the radius of sphere 1, so
R' = 2R
and so its moment of inertia is
So, the moment of inertia of sphere 2 is 4 times the moment of inertia of sphere 1.