Question

What's the moment of inertia of a solid cube of side lenght 'a' and mass 'm' "ABOUT IT'S BODY DIAGONAL"?

Answer 1

Answer:

This is the source of your confusion. The moment of inertia of a solid, uniform density cube about any axis that passes through the center of the cube is I=16ml2, where m is the mass of the cube and l is the length of any one of the cube's sides. Since the mass of a solid, uniform density cube is given by m=ρl3, another way to write the moment of inertia for such a cube is I=16ρl5. This means that the moment of inertia of your 2x2x2 cube will be 32 times that of the moment of inertia of your 1x1x1 cube.

You will get exactly the same result (a factor of 32) if you consider that 2x2x2 cube to consist of eight 1x1x1 cubes and apply the parallel axis theorem.