In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A : A uniform circular motion have non uniform acceleration .
R: The direction of acceleration of a particle in uniform circular motion changes continuously .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1) .
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false then mark (3).
D. If both Assertion and Reason are false statements then mark (4) .

Answer

To analyze the statements of assertion (A) and reason (R), we will break down the concepts of uniform circular motion and acceleration 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. This means that while the speed (magnitude of velocity) remains constant, the direction of the velocity vector is continuously changing.

**Hint**: Recall that speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

2. **Acceleration in Circular Motion**:
- Even though the speed is constant, the change in direction of the velocity means that there is an acceleration acting on the object. This acceleration is called centripetal acceleration, which always points towards the center of the circular path.

**Hint**: Remember that acceleration is defined as the rate of change of velocity, which includes changes in direction.

3. **Centripetal Acceleration**:
- The formula for centripetal acceleration (a) is given by:
\[ a = \frac{v^2}{r} \]
where \(v\) is the constant speed of the object and \(r\) is the radius of the circular path.

**Hint**: Think about how the radius of the circle and the speed of the object affect the acceleration.

4. **Nature of Acceleration**:
- Although the magnitude of the centripetal acceleration remains constant (since both \(v\) and \(r\) are constant), the direction of the acceleration vector is continuously changing as the object moves around the circle.

**Hint**: Visualize the circular path and how the direction of the acceleration vector changes at different points along the path.

5. **Assertion and Reason Analysis**:
- **Assertion (A)**: "A uniform circular motion has non-uniform acceleration." This statement is true because the direction of the acceleration is changing, even though its magnitude remains constant.
- **Reason (R)**: "The direction of acceleration of a particle in uniform circular motion changes continuously." This statement is also true, as explained above.

**Hint**: Evaluate both statements independently to determine if they are true or false.

6. **Conclusion**:
- Since both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion, we conclude that both statements are correct and that the reason is a valid explanation for the assertion.

**Hint**: When analyzing assertion and reason statements, always check if the reason logically supports the assertion.

### Final Answer:
Both the assertion (A) and the reason (R) are correct, and the reason is the correct explanation for the assertion.