(A) : The speed of particle remains constant in uniform circular motion
(R ) : No force is acting on the particle in uniform circular motion.

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
C. (A) is true but ( R) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze the assertion and the reason provided:

### Step 1: Understand the Assertion
The assertion states that "The speed of a particle remains constant in uniform circular motion."

- In uniform circular motion, the particle moves along a circular path with a constant speed. This means that the magnitude of the velocity (which is speed) does not change as the particle moves around the circle.

### Step 2: Analyze the Reason
The reason states that "No force is acting on the particle in uniform circular motion."

- This statement is incorrect. In uniform circular motion, even though the speed is constant, the direction of the velocity is continuously changing. This change in direction means that there is an acceleration acting on the particle, known as centripetal acceleration, which is directed towards the center of the circular path.

### Step 3: Identify the Force
Since there is centripetal acceleration, there must be a force acting on the particle. This force is called the centripetal force, which is responsible for keeping the particle in its circular path.

### Step 4: Conclusion
- The assertion is true because the speed of the particle remains constant in uniform circular motion.
- The reason is false because a force (centripetal force) is indeed acting on the particle to maintain its circular motion.

Thus, we conclude that the assertion is true and the reason is false.

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

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