The moment of inertia of a body about a given axis of rotation depends upon :-

Options

A. the distribution of mass
B. distance of particle of body from the axis of rotation
C. shape of the body
D. all of the above2

Answer

To determine how the moment of inertia of a body about a given axis of rotation depends on various factors, we can break down the concept into several key components.

### Step-by-Step Solution:

1. **Definition of Moment of Inertia**:
The moment of inertia (I) of a body about an axis is a measure of how difficult it is to change its rotational motion about that axis. It depends on the mass distribution of the body relative to the axis of rotation.

2. **Factors Affecting Moment of Inertia**:
The moment of inertia depends on:
- The **mass** of the body (m).
- The **distribution** of that mass relative to the axis of rotation.
- The **distance** of each mass element from the axis of rotation.

3. **Mathematical Representation**:
The moment of inertia can be mathematically expressed as:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of the i-th particle and \( r_i \) is the perpendicular distance of that mass from the axis of rotation. This shows that I is proportional to both the mass and the square of the distance from the axis.

4. **Conclusion**:
Therefore, the moment of inertia depends on:
- The **total mass** of the body.
- The **distribution of mass** (how the mass is spread out).
- The **shape of the body** (which affects the distances of mass elements from the axis).
- The **axis of rotation** itself.

5. **Final Answer**:
Thus, the correct answer is that the moment of inertia depends on all of the above factors. If this is a multiple-choice question, the option that states "all of the above" would be the correct choice.