A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T 1 and (ii) back and forth in a direction perpendicular to its plane, with a period T 2 . The ratio T 1 T 2 will be :

Step-by-step solution

The time period of oscillation of physical pendulum is given by T = 2 π I M g l     . . . ( 1 ) Where, I is the moment of inertia of ring about given axis and l is the distance of centre of mass of ring from the axis of rotation. Moment of inertia of ring in its plane is given by I 1 = I c +   M d 2 = M R 2 + M R 2 = 2 M R 2 Moment of inertia of ring perpendicular to its plane is given by I 2 = I c +   M d 2 = M R 2 2 + M R 2 = 3 2 M R 2 Now the ratio of time period is given by T 1 T 2 = I