Assertion In circular motion, average speed and average velocity are never equal.
Reason In any curvilinear path, these two are never equal.

Options

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

Answer

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

### Step 1: Understand the Assertion
The assertion states that in circular motion, average speed and average velocity are never equal.

- **Average Speed** is defined as the total distance traveled divided by the total time taken.
- **Average Velocity** is defined as the total displacement (the shortest distance from the initial to the final position) divided by the total time taken.

In circular motion, the object moves along a curved path and returns to its starting point. Therefore, the total displacement is zero (since the initial and final positions are the same), while the total distance traveled is equal to the circumference of the circle.

### Step 2: Calculate Average Speed and Average Velocity
- **Average Speed**: If the radius of the circle is \( r \) and the object completes one full revolution, the distance traveled is \( 2\pi r \). If the time taken for one revolution is \( T \), then:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2\pi r}{T} \]

- **Average Velocity**: Since the displacement is zero (the object returns to its starting point), the average velocity is:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0}{T} = 0 \]

### Step 3: Conclusion on the Assertion
Since the average speed is a positive value (greater than zero) and the average velocity is zero, they are indeed never equal. Therefore, the assertion is true.

### Step 4: Understand the Reason
The reason states that in any curvilinear path, average speed and average velocity are never equal.

This is also true because, in any curvilinear motion, the total distance traveled will always be greater than or equal to the total displacement (which is the straight-line distance between the starting and ending points). Hence, the average speed will be greater than the average velocity unless the object does not move (in which case both would be zero).

### Final Conclusion
Both the assertion and the reason are true, and the assertion is supported by the reasoning provided.

### Final Answer
- **Assertion**: True
- **Reason**: True