The radius of gyration (K) of a rigid body changes with change of :-

Options

A. Angular speed
B. Axis of rotation
C. Both (1) and (2)
D. Never changes

Answer

To solve the question regarding the radius of gyration (K) of a rigid body and how it changes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Radius of Gyration (K)**:
- The radius of gyration (K) is defined as the distance from the axis of rotation at which the entire mass of the body can be assumed to be concentrated without changing the moment of inertia (I).
- Mathematically, it is expressed as:
\[ K = \sqrt{\frac{I}{m}} \]
where \(I\) is the moment of inertia and \(m\) is the mass of the body.

2. **Moment of Inertia (I)**:
- The moment of inertia (I) of a rigid body depends on the mass distribution relative to the axis of rotation. It is calculated using the formula:
\[ I = \sum m_i r_i^2 \]
where \(m_i\) is the mass of the individual particles and \(r_i\) is the distance of each particle from the axis of rotation.

3. **Effect of Changing the Axis of Rotation**:
- When the axis of rotation changes, the distances \(r_i\) of the mass elements from the new axis will change. This will result in a different moment of inertia (I) for the body.
- Since the radius of gyration (K) is derived from the moment of inertia (I), any change in I due to a change in the axis of rotation will also affect K.

4. **Conclusion**:
- Therefore, the radius of gyration (K) changes with a change in the axis of rotation. It does not depend on other factors such as angular speed.

### Final Answer:
The radius of gyration (K) of a rigid body changes with a change of the **axis of rotation**.