The radius of gyration of a body depends upon

Options

A. shape and size of body
B. nature of mass distribution of body
C. choice of axis of rotation
D. All of the above

Explanation

To determine what the radius of gyration of a body depends upon, we can analyze the components involved in its definition and the factors that influence it.

### Step-by-Step Solution:

1. **Understanding Radius of Gyration**:
The radius of gyration (k) is defined 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**:
The moment of inertia \(I\) depends on the distribution of mass relative to the axis of rotation. It is calculated based on how the mass is distributed throughout the body.

3. **Factors Influencing Moment of Inertia**:
- **Nature of Mass Distribution**: The way mass is distributed within the body affects the moment of inertia. For example, a solid disc and a hollow disc of the same mass and radius will have different moments of inertia.
- **Choice of Axis of Rotation**: The moment of inertia changes when the axis of rotation changes. For instance, rotating around an axis through the center versus an axis at the edge will yield different moments of inertia.

4. **Shape and Size of the Body**:
The shape and size also play a crucial role in determining the moment of inertia. Different geometries (like a sphere, cylinder, or cube) have different formulas for calculating their moments of inertia.

5. **Conclusion**:
Since the radius of gyration is derived from the moment of inertia, it will depend on:
- The nature of mass distribution
- The choice of axis of rotation
- The shape and size of the body

Therefore, the radius of gyration depends on all of the above factors.

### Final Answer:
The radius of gyration of a body depends upon:
- Shape and size of the body
- Nature of mass distribution of the body
- Choice of axis of rotation
- Hence, the correct answer is **all of the above**.

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