A uniform thin rod of length L is pivoted at a point P located at a distance 4L from one end. The axis is perpendicular to the rod and passes through P.
(i) Obtain an expression for the moment of inertia of the rod about the pivot axis in terms of M and L.
(ii) Hence derive the corresponding radius of gyration kP.
(iii) Express kP as a fraction of the rod length L.