Three homogeneous bodies, each of total mass M and outer radius R, are described below. All are able to rotate about the central axis (symmetry axis through the centre and perpendicular to the plane).
Body 1 : a solid disc.
Body 2 : a thin circular ring.
Body 3 : a composite wheel made by combining a solid disc of mass 2M with a concentric thin ring of mass 2M at the rim of radius R.
(i) Derive an expression for the moment of inertia of Body 3 about the stated axis in terms of M and R.
(ii) Calculate the moments of inertia of Body 1 and Body 2 about the same axis.
(iii) Arrange the three bodies in descending order of their moments of inertia.
(iv) Provide a qualitative justification for the order obtained, referring explicitly to how the placement of mass affects the radius of gyration.