Assertion: Value of radius of gyration of a uniform rigid body depends on axis of rotation. Reason: Radius of gyration is root mean square distance of particles of the body from the axis of rotation.

Question

Assertion: Value of radius of gyration of a uniform rigid body depends on axis of rotation. Reason: Radius of gyration is root mean square distance of particles of the body from the axis of rotation. (A) If both assertion and reason are true and reason is the correct explanation of assertion (B) If both assertion and reason are true but reason is not the correct explanation of assertion (C) If assertion is true but reason is false (D) If both assertion and reason are false

Tardigrade Admin · Accepted Answer

Radius of gyration of a body about a given axis is equal to

K = \frac{r _{1}^{2} + r _{2}^{2} + ...... r _{n}^{2}}{n}

It thus depends upon shape and size of the body, position and configuration of the axis of rotation and also on distribution of mass of body w.r.t. the axis of rotation.

Q. Assertion : Value of radius of gyration of a uniform rigid body depends on axis of rotation. Reason : Radius of gyration is root mean square distance of particles of the body from the axis of rotation.

If both assertion and reason are true and reason is the correct explanation of assertion

If both assertion and reason are true but reason is not the correct explanation of assertion

If assertion is true but reason is false

If both assertion and reason are false

Radius of gyration of a body about a given axis is equal to K=nr12​+r22​+......rn2​​​ It thus depends upon shape and size of the body, position and configuration of the axis of rotation and also on distribution of mass of body w.r.t. the axis of rotation.

Q. Assertion : Value of radius of gyration of a uniform rigid body depends on axis of rotation.
Reason : Radius of gyration is root mean square distance of particles of the body from the axis of rotation.

Radius of gyration of a body about a given axis is equal to
$K = \frac{r _{1}^{2} + r _{2}^{2} + ...... r _{n}^{2}}{n}$
It thus depends upon shape and size of the body, position and configuration of the axis of rotation and also on distribution of mass of body w.r.t. the axis of rotation.