Moment of inertia of body depends upon

Options

A. mass of the body
B. axis of rotation of the body
C. shape and size of the body
D. all of these

Explanation

To determine the factors on which the moment of inertia of a body depends, we can analyze the concept of moment of inertia step by step.

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
- The moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. It depends on how the mass is distributed relative to the axis of rotation.

2. **Formula for Moment of Inertia**:
- The moment of inertia is defined mathematically as:
\[ I = \sum m_i r_i^2 \]
where \(m_i\) is the mass of the ith particle and \(r_i\) is the perpendicular distance from the axis of rotation to the particle.

3. **Factors Affecting Moment of Inertia**:
- **Mass of the Body**: The greater the mass, the greater the moment of inertia. This is because more mass means more resistance to changes in motion.
- **Axis of Rotation**: The moment of inertia varies depending on the axis about which the body rotates. Different axes will yield different distances (r) for the mass elements, thus changing the moment of inertia.
- **Shape and Size of the Body**: The distribution of mass in relation to the axis of rotation is crucial. Different shapes (like a solid cylinder vs. a hollow cylinder) with the same mass can have different moments of inertia due to how the mass is distributed.

4. **Conclusion**:
- Therefore, the moment of inertia depends on:
- The mass of the body
- The axis of rotation
- The shape and size of the body
- Hence, the correct answer is that the moment of inertia depends on all of these factors.

### Final Answer:
The moment of inertia of a body depends on:
- Mass of the body
- Axis of rotation of the body
- Shape and size of the body
- **All of these factors (Option D)**.