Assertion `:-` Work done by frictional force may be sometimes path independent.
Reason`:-` Frictional force is a non`-`conservative force.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Answer

To analyze the given assertion and reason, we will break down the concepts of work done by friction and the nature of frictional forces.

### Step-by-Step Solution:

1. **Understanding Work Done by Friction**:
- Work done (W) by a force is defined as the dot product of the force (F) and the displacement (d) of the point of application of the force:
\[ W = F \cdot d = F \cdot |d| \cos(\theta) \]
- Here, \(\theta\) is the angle between the force and the displacement vector.

2. **Path Independence of Work Done**:
- Work done by a force is path independent if it does not depend on the specific path taken between two points. For friction, this typically means that the work done is zero or constant regardless of the path.

3. **Example of Pure Rolling**:
- In pure rolling motion, the point of contact between the rolling object and the surface does not slide. Therefore, the displacement of the point of contact is zero.
- Since the work done is calculated based on the displacement of the point of application of the force, the work done by friction in this case is:
\[ W = F \cdot 0 = 0 \]
- Thus, the work done by friction in pure rolling is zero, making it path independent.

4. **Example of Uniform Circular Motion**:
- In uniform circular motion, the frictional force acts towards the center of the circular path, while the displacement of the object is tangential to the path.
- The angle between the frictional force and the displacement is 90 degrees, which means:
\[ W = F \cdot d \cdot \cos(90^\circ) = 0 \]
- Again, the work done by friction is zero, indicating path independence.

5. **Nature of Frictional Force**:
- Friction is classified as a non-conservative force because its work done depends on the path taken. In general scenarios, the work done by friction can vary based on the distance and the nature of the surface.

6. **Conclusion**:
- The assertion that "Work done by frictional force may be sometimes path independent" is true in specific cases like pure rolling and uniform circular motion.
- The reason "Frictional force is a non-conservative force" is also true, but it does not correctly explain the assertion because non-conservative forces typically have path-dependent work.

### Final Evaluation:
- **Assertion**: True
- **Reason**: True, but not the correct explanation for the assertion.