A ring of the radius r is suspended from a point on its circumference. If the ring is made to oscillate in the plane of the figure, then the angular frequency of these small oscillations is

Step-by-step solution

It is a physical pendulum, the time period of which is, T = 2 π I mgl Here, I = moment of inertia of the ring about the point of suspension = m r 2 + m r 2 = 2 m r 2 ​and l = distance of the point of suspension from the centre of gravity = r ∴ T = 2 π 2 mr 2 mgr = 2 π 2r g ∴ Angular frequency ω = 2 π T or ω = g 2r