A thin straight rod of fixed length L and total mass M can have its material distributed in different ways while the length remains unchanged.
(i) Explain qualitatively how the moment of inertia of the rod about an axis through its centre and perpendicular to its length will change if more of the mass is shifted towards the ends while keeping M and L constant.
(ii) Keeping M and L unchanged, the rod is now modified so that extra metal is added near the ends and an equal amount is removed near the centre. Predict whether the radius of gyration about the same axis will increase, decrease or remain the same and justify your answer.