In uniform circular motion assuming `vecV` - Velocity,`vec r`= radius vector , `vecomega`= angular velocity relative to centre of the circle, `veca=` acceleration, which of the following is/are correct?

Options

A. `|Deltavecv| ne 0` but `Delta|vecv|=0`
B. `|Deltavecomega|=0` and `Delta|vecomega|=0`
C. `|Deltavecr| ne 0` but `Delta|vecr| = 0`
D. `|Deltaveca| ne 0` but `Delta|veca| = 0`

Answer

To solve the question regarding uniform circular motion and determine which statements about velocity, radius vector, angular velocity, and acceleration are correct, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding Uniform Circular Motion**:
- In uniform circular motion, an object moves in a circular path with a constant speed. However, the direction of the velocity vector changes continuously.

2. **Velocity**:
- The magnitude of the velocity (speed) remains constant, but the direction changes. Therefore, the vector form of velocity is not constant.
- **Conclusion**: The magnitude of the velocity is constant, but the velocity vector itself is changing.

3. **Angular Velocity**:
- Angular velocity (ω) is defined as the rate of change of angular displacement and is constant in uniform circular motion.
- **Conclusion**: Angular velocity is constant.

4. **Radius Vector**:
- The radius vector (r) is the vector from the center of the circle to the object. In uniform circular motion, the radius remains constant in magnitude, but its direction changes as the object moves around the circle.
- **Conclusion**: The magnitude of the radius vector is constant, but the radius vector itself is changing.

5. **Acceleration**:
- In uniform circular motion, there is a centripetal acceleration directed towards the center of the circle. The magnitude of this acceleration is constant, but its direction changes as the object moves.
- **Conclusion**: The magnitude of acceleration is constant, but the acceleration vector itself is changing.

6. **Summary of Statements**:
- **Magnitude of velocity is constant**: True
- **Velocity vector is changing**: True
- **Angular velocity is constant**: True
- **Magnitude of radius vector is constant**: True
- **Radius vector is changing**: True
- **Magnitude of acceleration is constant**: True
- **Acceleration vector is changing**: True

### Final Evaluation:
- The statements regarding the uniform circular motion can be summarized as follows:
- The magnitude of velocity is constant, but the velocity vector changes.
- Angular velocity is constant.
- The magnitude of the radius vector is constant, but the radius vector itself changes.
- The magnitude of acceleration is constant, but the acceleration vector changes.