In which of the following cases the, potential energy is defined?

Options

A. both conservative and non-conservative forces
B. conservative force only
C. non-conservative force only
D. Neither conservative nor-conservative forces

Explanation

To determine in which cases potential energy is defined, we need to understand the nature of forces involved. Here’s a step-by-step solution:

### Step 1: Understand Potential Energy
Potential energy is the energy stored in an object due to its position in a force field, such as gravitational or elastic fields. It is defined in relation to conservative forces.

### Step 2: Identify Conservative Forces
Conservative forces are those forces for which the work done is independent of the path taken and depends only on the initial and final positions. Examples include gravitational force and spring force.

### Step 3: Analyze the Options
- **Option A**: Both conservative and non-conservative forces.
- This is incorrect because potential energy is not defined for non-conservative forces, as they depend on the path taken.

- **Option B**: Conservative forces only.
- This is correct because potential energy is defined only in the context of conservative forces.

- **Option C**: Non-conservative forces only.
- This is incorrect as potential energy cannot be defined in the context of non-conservative forces.

- **Option D**: Neither conservative nor non-conservative forces.
- This is also incorrect because potential energy is indeed defined for conservative forces.

### Step 4: Conclusion
Based on the analysis, the correct answer is **Option B: Conservative forces only**.