Question

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

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

Answer 1

Answer: (B), (C)

The correct options are
B You can find two points in the body in a plane perpendicular to the axis of rotation having the same acceleration.
C Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is the same.

In the fixed axis rotation we see that every point on the body has two components of velocity, one in the radial direction and on in the tangential direction. The resultant of these velocities is not same for any two points lying in the plane of the body.
Any two points on the radial line have the radial acceleration directed towards the center of equal magnitude and the the tangential acceleration of equal magnitude as well. Thus option B is correct.
All the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation have the same speed but different velocities.