M.I. of a body doesn't depend upon

Options

A. angular velocity of the body,
B. mass of the body.
C. distribution of mass in the body.
D. axis of rotation of the body.

Answer

To solve the question regarding the moment of inertia (M.I.) of a body and what it does not depend on, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Moment of Inertia (M.I.):**
- Moment of inertia is a measure of an object's resistance to changes in its rotation about an axis. It is calculated by considering the mass distribution of the object relative to the axis of rotation.

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

3. **Identifying Factors that Affect M.I.:**
- From the formula, we can see that the moment of inertia depends on:
- The mass of the body (M).
- The distribution of that mass relative to the axis of rotation (the distances \(r\)).

4. **Analyzing the Options Given:**
- The question asks which factor does not affect the moment of inertia. The options typically include:
- A) Angular velocity
- B) Mass of the body
- C) Distribution of mass
- D) Axis of rotation
- We need to determine which of these does not influence the moment of inertia.

5. **Evaluating Each Option:**
- **A) Angular velocity:** Moment of inertia does not depend on angular velocity. It is a property of the mass distribution and does not change with how fast the body is rotating.
- **B) Mass of the body:** Moment of inertia directly depends on the mass of the body.
- **C) Distribution of mass:** Moment of inertia is affected by how the mass is distributed relative to the axis of rotation.
- **D) Axis of rotation:** The moment of inertia changes with the axis of rotation since it affects the distances \(r\).

6. **Conclusion:**
- The factor that does not affect the moment of inertia is **A) Angular velocity**.

### Final Answer:
The moment of inertia of a body does not depend on **angular velocity**.

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