Assertion : If a particle is rotating in a circle, then angular momentum about centre is mvR
Reason : In circular motion, angular momentum about centre is always constant.

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states: "If a particle is rotating in a circle, then angular momentum about the center is \( mvR \)."
- In circular motion, the angular momentum \( L \) of a particle about a point (in this case, the center) is given by the formula:
\[ L = r \times p \]
where \( p \) is the linear momentum of the particle, \( p = mv \) (mass times velocity).

2. **Calculating Angular Momentum**:
- The position vector \( r \) is the radius of the circle, and since the motion is circular, the velocity vector \( v \) is always tangential to the circle.
- The angle \( \theta \) between the position vector \( r \) and the velocity vector \( v \) is \( 90^\circ \) (or \( \frac{\pi}{2} \) radians) because they are perpendicular.
- Therefore, the magnitude of angular momentum can be calculated as:
\[ L = r \cdot mv \cdot \sin(\theta) = mvR \cdot \sin(90^\circ) = mvR \]
- This confirms that the assertion is correct.

3. **Understanding the Reason**:
- The reason states: "In circular motion, angular momentum about the center is always constant."
- In circular motion, both the magnitude and direction of the angular momentum remain constant. The magnitude remains constant because \( mvR \) does not change as long as the mass \( m \), velocity \( v \), and radius \( R \) are constant.
- The direction of angular momentum is also constant as it is always perpendicular to the plane of motion (out of the plane if we consider a horizontal circle).

4. **Conclusion**:
- Both the assertion and the reason are true. The assertion correctly states the formula for angular momentum in circular motion, and the reason correctly states that angular momentum remains constant in circular motion.

### Final Answer:
- Both Assertion and Reason are true, and the reason correctly explains the assertion.