Paragraph: One twirls a circular ring (of mass M and radius R ) near the tip of one's finger as shown in Figure 1 . In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r . The finger rotates with an angular velocity ₀ . The rotat

Step-by-step solution

V C M of Ring =   ( R - r )   ω 0 For no slipping R ω 1 - R - r w 0 = r ω 0 R ω 1 - R ω 0 = 0 KE of ring = 1 2 M R - r 2   ω 0 2 + 1 2 m R 2 ω 0 2 Which is not matching with any answer given if r ≪ R But we take R ω 0   ≈ R - r ω 0 Then K E   ≈ 2 2 M   R - r 2     ω 0 2 Then M ω 0 2 R - r 2 is nearest possible option