Which of the following force is not conservative :-

Options

A. `bar(F)=3hati+4hatj`
B. `bar(F)=3xhati+4yhatj`
C. `bar(F)=3yhati+4xhatj`
D. `bar(F)=3x^(2)hati+4y^(2)hatj`

Answer

To solve the question of which of the following forces is not conservative, we need to understand the characteristics of conservative and non-conservative forces.

### Step-by-Step Solution:

1. **Understanding Conservative Forces**:
- A conservative force is one where the work done by the force on an object moving from one point to another is independent of the path taken. The work done only depends on the initial and final positions.
- Examples include gravitational force and spring force.

2. **Understanding Non-Conservative Forces**:
- A non-conservative force is one where the work done depends on the path taken. The work done can vary based on the route taken between two points.
- Examples include frictional force and air resistance.

3. **Identifying the Forces**:
- We need to analyze the given options (not provided in the question, but typically they would be forces like gravitational, frictional, spring, etc.) and determine which one does not meet the criteria of a conservative force.

4. **Analyzing the Given Forces**:
- If a force is represented as \( F = f(x) \hat{i} + g(y) \hat{j} \), we can check if it is conservative by examining the functions \( f(x) \) and \( g(y) \).
- If \( f(x) \) and \( g(y) \) are polynomials or constants, the force is likely conservative.
- If the force has terms that depend on the path (like friction, which is dependent on the surface and distance), it is non-conservative.

5. **Conclusion**:
- Based on the analysis, we determine which of the forces listed is non-conservative. According to the video transcript, the force represented by option C is identified as non-conservative.

### Final Answer:
- The force that is not conservative is **C**.