A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement(s) are true?

Options

A. You can find two points in the body in a plane perpendicular to the axis of rotation having same velocity
B. you can find two points in the body in a plane perpendicular to the axis of rotation having same acceleration
C. speed of fall the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is same
D. angular speed of the body is same as seen from any points in the body

Answer

C, D

Explanation

All points in the body, in plane perpendicular to the axis of rotation, revolve in concentric circles. All points lying on the circle of same radius have same speed (and also same magnitude of acceleration) but different directions of velocity (also different directions of acceleration) hence there cannot be two points in the given plane with same velocity or with same acceleration. As mentioned above, points lying on circle of same radius have same speed. Angular speed of body at any instant wrt any point on the body is same by definition.