(A): When a particle moves in a circle with a uniform speed, its velocity and accele ration both changes.
(R): The centripetal acceleration in circular motion is dependent on angular velocity of the body.

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. Both (A) and (R) are fals

Answer

To solve the question, we need to analyze both statements (A) and (R) regarding circular motion.

### Step 1: Analyze Statement (A)
Statement (A) claims that when a particle moves in a circle with uniform speed, its velocity and acceleration both change.

- **Explanation**:
- In circular motion, even if the speed (magnitude of velocity) is constant, the direction of the velocity vector is continuously changing.
- Since velocity is a vector quantity (having both magnitude and direction), a change in direction means that the velocity is changing.
- Similarly, the acceleration in circular motion (centripetal acceleration) is directed towards the center of the circle and also changes direction as the particle moves along the circular path.

### Step 2: Analyze Statement (R)
Statement (R) states that the centripetal acceleration in circular motion is dependent on the angular velocity of the body.

- **Explanation**:
- The formula for centripetal acceleration (Ac) is given by \( A_c = r \omega^2 \), where \( r \) is the radius of the circular path and \( \omega \) is the angular velocity.
- This shows that centripetal acceleration indeed depends on the angular velocity of the body.

### Step 3: Determine the Relationship Between (A) and (R)
Now we need to evaluate whether (R) provides a correct explanation for (A).

- **Evaluation**:
- While both statements are true, (R) does not adequately explain why the velocity and acceleration change in (A).
- The change in velocity and acceleration in circular motion is primarily due to the change in direction, not directly because of the dependence on angular velocity.

### Conclusion
Based on the analysis:
- Statement (A) is true.
- Statement (R) is true but does not explain (A).
- Therefore, the correct answer is that both A and R are true, but R is not the correct explanation of A.

### Final Answer
Both A and R are true, but R is not the correct explanation of A.

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