Question

Define the radius of gyration and write its physical significance.

Answer 1

Hint: The distance from an axis at which the mass of a body may be assumed to be concentrated and at which the moment of inertia will be equal to the moment of inertia of the actual mass about the axis, equal to the square root of the quotient of the moment of Inertia and the mass.

Complete step by step answer:
Radius of gyration is defined as the distance axis of rotation to a point where the total body is supposed to concentrate.
Moment of inertia \[\text{I}=\text{m}{{\text{k}}^{\text{2}}}\]
Where, M = mass of body
K = Radius of Gyration
SI unit of Radius of gyration is meter.

Physical significance:
1. If the particles of the body are distributed close to the axis of rotation, the radius of gyration is less.
2. If the particles are distributed away from the axis of rotation, the radius of gyration is more.

Note:
The knowledge of mass and radius of gyration of the body about a given axis of rotation gives the value of its moment of inertia about the same axis, even if we do not know the actual shape of the body.