Question

A ring and a disc having masses in the ratio 1:2 are made to rotate about their central axes. Both are acted upon by the same torque when they are at rest. Which one will have more angular velocity when torque has been removed from both after the same time? Both have the same radius.

(a) Ring

(b) Disc

(c) Same for both

(d) Depends on ratio of mass and radius

The question was asked by my school principal while I was bunking the class.

I would like to ask this question from Angular Momentum in case of Rotations about a Fixed Axis topic in section System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Right choice is (c) Same for both

The explanation is: The angular momentum for each will be the same as torque is the same.                                 Let the mass of the ring be m, and their radius be ‘R’. The ratio of angular speeds will be the inverse ratio of their moments of inertia.                                                                                                                                                 Moment of inertia of ring = mR^2& moment of inertia of disc = 2mR^2/2 = mR^2. As their moment of inertia is the same their angular speeds will be the same.