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

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You can find two points in the body in a plane perpendicular to the axis of rotation having the same acceleration.

Angular speed of the body is the same as seen from any point in the body.

Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is the same.

You can find two points in the body in a plane perpendicular to the axis of rotation having the same velocity.

answer is C, D.

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Detailed Solution

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 w.r.t. any point on the body is same by definition.

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