A uniform circular ring is suspended from a thin torsion wire whose torsional constant (restoring torque per unit angular twist) is 0.05N m rad−1. When the ring is given a small twist about its central vertical axis, it executes torsional oscillations with a period of 2.0s. The mean radius of the ring is 0.15m.
(i) Write the relation connecting the period of a torsional pendulum, its moment of inertia and the torsional constant of the wire.
(ii) Using the given data, calculate the moment of inertia of the ring about the axis of oscillation.
(iii) Hence determine the mass of the ring.
(iv) Compute the radius of gyration of the ring about the same axis and compare it with the given radius.