Which of the following statements is not true?

Options

A. Work done by conservative force on an object depends only on the initial and final states and not on the path taken.
B. The change in potential energy of a system corresponding to conservative intermal force is equal to negative of the work done by these forces.
C. If some of the internal force within a system are non-conservative, then the mechanical energy of the system is not constant.
D. If the internal forces are conservative, the work done by the internal forces is equal to the change in mechanical energy.

Explanation

To determine which statement is not true, we will analyze each statement one by one based on the principles of work, energy, and conservative/non-conservative forces.

### Step-by-Step Solution:

1. **Analyze Statement 1**:
- **Statement**: "Work done by conservative force on an object depends only on the initial and final states and not on the path taken."
- **Explanation**: By definition, conservative forces (like gravitational force) do not depend on the path taken. The work done is determined solely by the initial and final positions.
- **Conclusion**: This statement is **true**.

2. **Analyze Statement 2**:
- **Statement**: "The change in potential energy of a system corresponding to conservative internal force is equal to the negative of the work done by these forces."
- **Explanation**: When a conservative force does work, it changes the potential energy of the system. The work done by the conservative force is indeed equal to the negative change in potential energy (W = -ΔPE).
- **Conclusion**: This statement is **true**.

3. **Analyze Statement 3**:
- **Statement**: "If some of the internal forces within a system are non-conservative then the mechanical energy of the system is not constant."
- **Explanation**: Non-conservative forces (like friction) dissipate energy, meaning that mechanical energy is not conserved. Thus, if non-conservative forces are present, the total mechanical energy changes.
- **Conclusion**: This statement is **true**.

4. **Analyze Statement 4**:
- **Statement**: "If the internal forces are conservative, the work done by internal forces is equal to the change in mechanical energy."
- **Explanation**: If the internal forces are conservative, they do not dissipate energy. Instead, they convert energy between kinetic and potential forms without changing the total mechanical energy of the system. Therefore, the work done by conservative internal forces does not result in a change in the total mechanical energy.
- **Conclusion**: This statement is **not true**.

### Final Answer:
The statement that is not true is **Statement 4**.