A body is in pure rotation. The linear speed 'v' of a particle, the distance 'r' of the particle from the axis and the angular velocity `omega` of the body are related as `omega=v/r`. Thus

Options

A. `omega prop1/r`
B. `omegapropr`
C. `omega=0`
D. `omega` is independent of r

Answer

To solve the problem, we need to analyze the relationship between angular velocity (ω), linear speed (v), and the distance from the axis of rotation (r) in a body undergoing pure rotation.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We start with the given relationship:
\[ \omega = \frac{v}{r} \]
where:
- \( \omega \) = angular velocity
- \( v \) = linear speed of a particle
- \( r \) = distance of the particle from the axis of rotation

2. **Rearranging the Equation**:
We can rearrange the equation to express linear speed in terms of angular velocity and distance:
\[ v = \omega \cdot r \]

3. **Analyzing Angular Velocity**:
In pure rotation, the angular velocity \( \omega \) is constant for all particles in the body. This means that regardless of the distance \( r \) from the axis of rotation, the value of \( \omega \) does not change.

4. **Determining the Relationship**:
Since \( \omega \) is constant, we can conclude that:
- As \( r \) increases, \( v \) must also increase proportionally (since \( v = \omega \cdot r \)).
- However, \( \omega \) itself does not depend on \( r \).

5. **Conclusion**:
Therefore, we can conclude that angular velocity \( \omega \) is independent of the distance \( r \) from the axis of rotation.

### Final Answer:
From the analysis, we find that the correct option is:
- **Option 4**: \( \omega \) is independent of \( r \).