In which of the following cases can the work done increase the potential energy?

Options

A. (a) Both conservative and non-conservative forces
B. (b) Conservative force only
C. (c) Non-conservative force only
D. (d) Neither conservative nor non-conservative forces.

Explanation

To determine in which cases the work done can increase the potential energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Work and Potential Energy**:
- Work done by a conservative force is related to the change in potential energy. The relationship can be expressed as:
\[ W = -\Delta PE \]
- Here, \(W\) is the work done by the conservative force, and \(\Delta PE\) is the change in potential energy.

2. **Identify the Sign of Work Done**:
- If the work done by the conservative force is negative (\(W < 0\)), it indicates that the potential energy is increasing (\(\Delta PE > 0\)).
- Conversely, if the work done is positive (\(W > 0\)), it indicates that the potential energy is decreasing (\(\Delta PE < 0\)).

3. **Consider Non-Conservative Forces**:
- Non-conservative forces (like friction or air resistance) do not contribute to potential energy changes in the same way. Instead, they convert mechanical energy into other forms (like heat), which does not increase potential energy.

4. **Conclusion**:
- Therefore, for work done to increase potential energy, it must be done by a conservative force, where the work done is negative.

5. **Final Answer**:
- The only case where work done can increase potential energy is when the work is done by a conservative force.