The axis of rotation of a purely rotating body

Options

A. must pass thruogh the centre of mas
B. may pas through the centre of mass
C. must pass through a particle of the body
D. may pass through a paerticle of the body

Answer

To solve the question about the axis of rotation of a purely rotating body, let's analyze the options step by step.

### Step 1: Understanding the Concept of Purely Rotating Body
A purely rotating body is one that rotates around an axis without any translational motion. The axis of rotation can be defined in relation to the body's center of mass and its particles.

### Step 2: Evaluating the Options
1. **Option 1: Must pass through the center of mass**
- This statement suggests that the axis of rotation is fixed and must always go through the center of mass. However, this is not necessarily true for all purely rotating bodies. Therefore, this option is incorrect.

2. **Option 2: May pass through the center of mass**
- This statement indicates that the axis of rotation can pass through the center of mass, but it is not a requirement. This is a valid statement because there are cases where the axis of rotation does not coincide with the center of mass. Thus, this option is correct.

3. **Option 3: Must pass through a particle of the body**
- Similar to option 1, this statement implies a strict condition that the axis must pass through a particle of the body. This is not necessarily true, as the axis can be external to the body. Hence, this option is also incorrect.

4. **Option 4: May pass through a particle of the body**
- This statement suggests that the axis of rotation can pass through a particle of the body, but it is not mandatory. This is a valid statement as well, since the axis can be anywhere in relation to the particles of the body. Therefore, this option is correct.

### Conclusion
Based on the evaluation of the options:
- The correct answers are **Option 2** (may pass through the center of mass) and **Option 4** (may pass through a particle of the body).

### Final Answer
The axis of rotation of a purely rotating body may pass through the center of mass and may pass through a particle of the body.

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