Suspended from a nail in a wall, a closed circular wire experiences small oscillations with an amplitude of 2^ and a time period of 2 s . Calculate the radius of the circular wire. Take g = ^2 m/s ^2 .

Step-by-step solution

The time period of small oscillations for a physical pendulum is given by T = 2 I mgd , where I is the moment of inertia about the axis of rotation and d is the distance from the point of suspension to the center of mass. For a circular wire (ring) of mass m and radius R suspended from a point on its circumference and oscillating in its own plane, the moment of inertia about the point of suspension is: I = I_ CM + mR^2 = mR^2 + mR^2 = 2mR^2 The distance from the point of suspension to the center of mass is d = R .