Assertion: Centripetal acceleration is always direction towards the centre of rotation of an object undergoing uniform circular motion
Reason: Centripetal acceleration is a constant vector

Explanation

To analyze the given assertion and reason, we will break down the concepts of centripetal acceleration and its characteristics in uniform circular motion.

### Step-by-Step Solution:

1. **Understanding Centripetal Acceleration**:
- Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It acts towards the center of the circular path.

2. **Assertion Analysis**:
- The assertion states that "Centripetal acceleration is always directed towards the center of rotation of an object undergoing uniform circular motion."
- This statement is true. In uniform circular motion, regardless of the position of the object on the circular path, the centripetal acceleration always points towards the center of the circle.

3. **Reason Analysis**:
- The reason states that "Centripetal acceleration is a constant vector."
- This statement is partially true. While the magnitude of centripetal acceleration (given by the formula \( a_c = \frac{v^2}{r} \)) remains constant if the speed \( v \) and radius \( r \) are constant, the direction of the centripetal acceleration vector changes continuously as the object moves along the circular path.

4. **Conclusion**:
- Since the assertion is true and the reason is not entirely correct (as it implies that the direction of the vector does not change), we conclude that:
- The assertion is true.
- The reason is false.

### Final Answer:
- Assertion: True
- Reason: False