The moment of inertia of a body depends upon

Options

A. mass only
B. angular velocity only
C. distribution of particles only
D. mass and distribution of mass about the axis

Answer

To determine the factors on which the moment of inertia of a body depends, we can break down the problem 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 is analogous to mass in linear motion.
- It is defined mathematically for a point mass as \( I = m \cdot r^2 \), where \( m \) is the mass of the particle and \( r \) is the perpendicular distance from the axis of rotation.

2. **Factors Affecting Moment of Inertia**:
- **Mass (m)**: The moment of inertia directly depends on the mass of the body. More mass means more inertia.
- **Distribution of Mass**: The way mass is distributed relative to the axis of rotation significantly affects the moment of inertia. For example, a mass further away from the axis contributes more to the moment of inertia than a mass closer to the axis.
- **Axis of Rotation**: The moment of inertia is also dependent on the axis about which it is calculated. Different axes will yield different moments of inertia for the same body.

3. **Analyzing the Options**:
- **Option A: Mass only** - Incorrect, as it does not consider the distribution of mass or the axis of rotation.
- **Option B: Angular velocity** - Incorrect, as the moment of inertia does not depend on angular velocity.
- **Option C: Distribution of particles only** - Incorrect, as it ignores the mass and the axis of rotation.
- **Option D: Mass and the distribution of mass about the axis** - Correct, as it encompasses both the mass of the body and how that mass is distributed in relation to the axis of rotation.

4. **Conclusion**:
- The correct answer is **Option D**: The moment of inertia of a body depends on mass and the distribution of mass about the axis.