Assertion Angle `(theta)` between a and v in circular motion is
`0^(@)lt thetalt180^(@)`
Reason Angle between any two vectors lies in the above range.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the angle \( \theta \) between the acceleration vector \( \mathbf{a} \) and the velocity vector \( \mathbf{v} \) in circular motion is in the range \( 0^\circ < \theta < 180^\circ \).
- This means that the angle can be any value greater than 0 degrees and less than 180 degrees.

2. **Understanding the Reason**:
- The reason states that the angle between any two vectors lies in the range \( 0^\circ < \theta < 180^\circ \).
- This is a general property of vectors, as the angle between two vectors can indeed vary from 0 degrees (when they point in the same direction) to 180 degrees (when they point in opposite directions).

3. **Analyzing the Circular Motion Context**:
- In circular motion, the velocity vector \( \mathbf{v} \) is always tangent to the path of the motion, while the acceleration vector \( \mathbf{a} \) can have both radial (centripetal) and tangential components.
- The radial acceleration is directed towards the center of the circular path, while the tangential acceleration can either increase or decrease the speed of the object moving in a circular path.

4. **Determining the Angle**:
- The angle \( \theta \) between \( \mathbf{a} \) and \( \mathbf{v} \) can indeed vary based on the direction of the tangential acceleration.
- If the tangential acceleration is in the same direction as the velocity, \( \theta \) will be less than 90 degrees. If it is in the opposite direction, \( \theta \) will be greater than 90 degrees and can go up to 180 degrees.

5. **Conclusion**:
- Both the assertion and the reason are true.
- However, the reason does not specifically explain why the angle between \( \mathbf{a} \) and \( \mathbf{v} \) in circular motion is constrained to the range \( 0^\circ < \theta < 180^\circ \). Therefore, while both statements are true, the reason does not adequately support the assertion.

### Final Answer:
- The assertion is true, the reason is true, but the reason does not correctly explain the assertion. Thus, the correct option is C.