Answer to Question #88857 in Mechanics | Relativity for Sridhar

Question

the case of pure rolling of a disc on rough horizontal surface the ratio of speed at top most point and the centre of mass is
1)2:1
2)1:2
3)1:1
4)√2:1

Answer 1

At every moment of time, the speed of the touching point is equal to zero, so that the disk is momentarily rotating around the axis passing through its touching point. For a rotational motion of a solid body, the speed of a point is directly proportional to its distance from the axis of rotation. Since the distance between the touching point and the top point is twice the distance between the touching point and the center of the disk (which is its center of mass), the speed of the top point is twice the speed of the center of the disk.

Answer: 1) 2:1.