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A rigid body is in pure rotation, that i...

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.

Text Solution

Verified by Experts

The correct Answer is:
C, D
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 hae sme speed (and also same magnitude of acceleration) but different direction of velocity (also different directions of acceleration).
Hence there cannot be tw points in the given plane wilth sme 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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A rigid body is rotating about a vertical axis at n rotations per minute, If the axis slowly becomes horizontal in t seconds and the body keeps on rotating at n rotations per minute then the torque acting on the body will be, if the moment of inertia of the body about axis of rotation is I.

For a particle of a rotating rigid body, v = r omega , which of the following are correct ?

Knowledge Check

  • S_(1) : Net torque on a system due to all internal force about any point is zero. S_(2) : For rigid body undergoing fixed axis rotation, the direction of its angular acceleration and angular velocity S_(3) : if net torque on a rigid body about its centre of mass is zero, the angular speed of the rigid body is always zero. S_(4) : For a rigid body undergoing fixed axis rotation abouts its centre of mass, then net torque on rigid body about any point is same.

    A
    TFFF
    B
    TTFT
    C
    FFFF
    D
    TFFT

  • A rigid body is rotating about a vertical axis at n rotations per minute, If the axis slowly becomes horizontal in t seconds and the body keeps on rotating at n rotations per minute then the torque acting on the body will be, if the moment of inertia of the body about axis of rotation is I.

    A
    zero
    B
    `(2pi nI)/(60t)`
    C
    `(2sqrt(2)pi nI)/(60t)`
    D
    `(4pi n I)/(60t)`

  • For a particle of a rotating rigid body, v = r omega , which of the following are correct ?

    A
    `omega prop (1)/(r )`
    B
    `omega prop v`
    C
    `v prop r`
    D
    `omega` is indepenedent of `r`