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 above

Answer

To determine the factors on which the moment of inertia of a body about a given axis of rotation depends, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
The moment of inertia (I) of a body about a given axis of rotation is defined as the sum of the products of the mass of each particle of the body and the square of its distance from the axis of rotation. Mathematically, it is expressed as:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of the particle and \( r_i \) is the distance from the axis of rotation.

2. **Factors Affecting Moment of Inertia**:
- **Mass Distribution**: The distribution of mass in the body plays a crucial role. If the mass is concentrated further away from the axis of rotation, the moment of inertia increases. For example, a denser part of the body will shift the center of mass towards that side, affecting the moment of inertia.
- **Distance from the Axis of Rotation**: The distance of each particle from the axis of rotation is squared in the moment of inertia formula. Therefore, the farther the mass is from the axis, the greater its contribution to the moment of inertia.
- **Shape of the Body**: The geometric shape of the body also influences the moment of inertia. Irregular shapes will have different mass distributions compared to regular shapes, leading to different moments of inertia.

3. **Conclusion**:
From the above analysis, we can conclude that the moment of inertia depends on:
- The distribution of mass within the body.
- The distance of the mass from the axis of rotation.
- The shape of the body.

4. **Final Answer**:
Therefore, the moment of inertia of a body about a given axis of rotation depends on all of the above factors. Hence, the correct answer is option D: all of the above.