Question

Is the radius of gyration a constant quantity?

Answer 1

Hint: The radius of gyration of a body about a rotational axis is the distance of a point from this axis at which the complete mass of the body is supposed to be concentrated such that the moment of inertia about the axis remains the same. The formula of the radius of gyration has to be known to give the answer to the given question. Note that the radius of gyration is related to the moment of inertia and mass of the system.

Complete answer:
Definition: The radius of gyration of a body is about an axis of rotation. It is defined as the spiral distance to the point that has a moment of inertia. The radius of gyration is a geometric characteristic of a body that is non-movable. The center of mass is an example of the radius of gyration.
The radius of gyration about an axis of rotation is calculated by using the formula $k = \sqrt {\dfrac{I}{M}} $, where $I$ is the moment of inertia, and $M$ is the mass of the system.
From the relation $k = \sqrt {\dfrac{I}{M}} $, it is seen that the radius of gyration depends on the moment of inertia, hence the axis of rotation and also the distribution of mass about the axis. Therefore, the radius of gyration is not constant.

Note:
A radius of gyration is the distance from the center of mass of an object at which the total mass is concentrated without changing its moment of rotational inertia about an axis through the center of mass.
A quantity is said to be a constant if its value does not change corresponding to any other quantity.
The point mass always lies perpendicular to the axis of rotation of the system, that is, the radius of gyration is always perpendicular to the axis of rotation.