In a uniform circular motion , the velocity, position vector and angular velocity are

Options

A. parallel to each other
B. mutually prependicular to each other
C. they are co-planer
D. the angle between them is `45^(@)`

Answer

To solve the question regarding the relationship between velocity, position vector, and angular velocity in uniform circular motion, we can break it down step by step.

### Step-by-Step Solution:

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

2. **Identifying the Vectors**:
- **Position Vector (r)**: This vector points from the center of the circle to the object. It represents the radius of the circle at any point in time.
- **Velocity Vector (v)**: This vector is tangent to the circular path at the object's position. It represents the instantaneous direction of motion.
- **Angular Velocity (ω)**: This vector represents the rate of change of angular displacement and points perpendicular to the plane of motion. Its direction can be determined using the right-hand rule.

3. **Analyzing the Relationships**:
- The position vector (r) and the velocity vector (v) are always perpendicular to each other. This is because the velocity is tangent to the circle, while the position vector points radially outward from the center.
- The angular velocity vector (ω) is also perpendicular to both the position vector and the velocity vector. It points in the direction determined by the right-hand rule (for clockwise motion, it points inward).

4. **Conclusion**:
- Since the position vector, velocity vector, and angular velocity vector are all mutually perpendicular to each other, we can conclude that they do not lie in the same direction (not parallel), are not coplanar, and the angle between them is not 45 degrees.

### Final Answer:
The correct option is that the velocity, position vector, and angular velocity are **mutually perpendicular to each other**.

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