Question

Radius of gyration depends upon:
A. Mass of the body
B. Nature of distribution of mass
C. Axis rotation
D. None of these

Answer 1

In this question we will find what radius of gyration is and in what factors it depends upon. Radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there.

Formula used:
${R_g} = \sqrt {\dfrac{I}{m}}$
Where, ${R_g}$ is the radius of gyration about an axis, $I$ is the moment of inertia around that axis and $m$ is the total mass.

Complete step by step answer:
Radius of gyration can be defined as the minimum distance to a point which would have a moment of inertia equal to the moment of inertia of the body's real distribution of mass, if the total mass of the body was assumed to be concentrated at that point.

Mathematically, the radius of gyration of a body about a given axis may also be defined as the root mean square distance of the various particles of the body from the axis of rotation.
We know that ${R_g} = \sqrt {\dfrac{I}{m}}$ . From this equation it can be observed that, radius of gyration depends on the moment of inertia of the body, mass of the body, shape and size of the body, and position of the axis of rotation.

Hence, we can say that option B and C are correct.

Note: Radius of gyration is useful in finding dynamic quantities of irregular shaped bodies in rotational mechanics. It is practically used in airplanes and other automobiles which need a balance. In such cases, the radius of gyration helps in doing calculations.Radius of gyration of a body is not constant and it does change with the change in location of the axis of rotation.