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 solve the problem, we need to analyze the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion
The assertion states that "A uniform circular motion has non-uniform acceleration."

- In uniform circular motion, the speed of the particle remains constant. However, even though the speed is constant, the direction of the velocity vector is continuously changing as the particle moves along the circular path.

### Step 2: Analyze the Type of Acceleration
In uniform circular motion, there are two types of acceleration to consider:
1. **Tangential Acceleration (at)**: This is responsible for changes in the speed of the particle. In uniform circular motion, the speed is constant, so tangential acceleration is zero (at = 0).
2. **Centripetal Acceleration (ac)**: This is directed towards the center of the circular path and is responsible for changing the direction of the velocity vector. It is given by the formula \( a_c = \frac{v^2}{r} \), where \( v \) is the constant speed and \( r \) is the radius of the circular path.

### Step 3: Conclusion on Assertion
Since the tangential acceleration is zero and the centripetal acceleration is present but does not change in magnitude (only in direction), we conclude that the assertion is misleading. The correct statement would be that uniform circular motion has constant acceleration in magnitude but changing direction.

### Step 4: Understand the Reason
The reason states that "The direction of acceleration of a particle in uniform circular motion changes continuously."

- This is true because the centripetal acceleration is always directed towards the center of the circle, and as the particle moves, this direction changes continuously.

### Step 5: Conclusion on Reason
The reason is correct and accurately describes the nature of acceleration in uniform circular motion.

### Final Conclusion
- The assertion (A) is **false** because it incorrectly states that uniform circular motion has non-uniform acceleration.
- The reason (R) is **true** because it correctly states that the direction of acceleration changes continuously.

### Final Answer
- Assertion (A) is false.
- Reason (R) is true.