Radius of gyration may be explained as the distance from the axis at which, if the entire mass of the object were to be concentrated, the moment of inertia would be the same about the given axis as with its real distribution of mass.
Let Consider a rigid object consists of n particles of every of the mass m. Let r1, r2, ...... rn be the perpendicular distances of these elements from the axis of motion. Then
Thus, radius of gyration of an object about an axis is similar to the root mean square distance of the constituent particles from the given axis.