Question

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

• 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 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 on the body.

Answer 1

Answer: (C), (D)

The correct options are
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 on the body.

All points in the body, on a plane perpendicular to the axis of rotation revolve in concentric circles. All points lying on a circle of the same radius have the same speed (and also the 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 the same velocity or with the same acceleraiton.

As mentioned above, points lying on a circle of same radius have same speed. For a cylindrical surface with the axis coinciding with axis of rotation, particles on the circle will move in circles of the same radius. Hence their speeds are the same.

Angular speed of body at any instant w.r.t. any point on body is the same by definition.

Options (c) and (d) are correct.