Work done by the conservative force on a system is equal to :

Options

A. (a) The change in kinetic energy of the system
B. (b) The change in potential energy of the system
C. (c) The change in total mechanical energy of the system
D. (d) None of the above

Explanation

To solve the question regarding the work done by a conservative force on a system, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Conservative Forces**:
- Conservative forces are forces where 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.

2. **Work Done by Conservative Force**:
- The work done \( W \) by a conservative force is related to the change in potential energy \( \Delta U \) of the system. The relationship is given by:
\[ W = -\Delta U \]
- This means that the work done by the conservative force is equal to the negative of the change in potential energy.

3. **Magnitude of Work and Potential Energy**:
- The magnitude of the work done by the conservative force is equal to the magnitude of the change in potential energy:
\[ |W| = |\Delta U| \]

4. **Work-Energy Principle**:
- If an external agent does work on the system against the conservative force, the potential energy of the system increases. This can be expressed as:
\[ W_{\text{external}} = -W_{\text{conservative}} = \Delta U \]
- Thus, if work is done against the conservative force, the potential energy increases.

5. **Conclusion**:
- Therefore, we conclude that the work done by the conservative force on a system is equal to the negative change in potential energy.

### Final Answer:
The work done by the conservative force on a system is equal to the negative of the change in potential energy:
\[ W = -\Delta U \]