Question

Define radius of gyration. Mention the factors on which it depends.

Answer 1

Hint: Radius of gyration is related to rotational mechanics. It finds its application while considering bodies of irregular shapes. It is related to the moment of inertia of the body and mass distribution within the body. Mathematical relation of radius of gyration can be used to recall the factors on which it depends.

Complete 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.
${{R}_{g}}=\sqrt{\dfrac{I}{m}}$
Where ${{R}_{g}}$, $I$ and $m$ are the radius of gyration about an axis, mass moment of inertia around that axis, and the total mass respectively.
From this relation it can be observed that, radius of gyration depends on moment of inertia of the body, mass of the body, shape and size of the body, and position of the axis of rotation.

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 a constant and it does change with the change in location of the axis of rotation.