One of the forces acting on the particle is conservative, then

Options

A. (a) Its work is zero when the particle moves exactly once around any closed path.
B. (b) Its work equals the change in the kinetic energy of the particle.
C. (c) It does not obey Newton's second law.
D. (d) Its work depends on the end points of the motion, not on the path in between.

Explanation

To solve the question regarding the properties of a conservative force acting on a particle, we can analyze each option provided.

### Step-by-Step Solution:

1. **Understanding Conservative Forces**:
A conservative force is defined as a force for which the work done in moving an object between two points is independent of the path taken. The work done by a conservative force in a closed path is always zero.

2. **Analyzing Option A**:
The statement is that the work done by a conservative force is zero when the particle moves once around any closed path.
- **Conclusion**: This is true because, by definition, the work done by a conservative force over a closed loop is zero.
- **Result**: Option A is correct.

3. **Analyzing Option B**:
The statement claims that the work done is equal to the change in kinetic energy of the particle.
- **Conclusion**: While the work-energy theorem states that the total work done on a particle is equal to its change in kinetic energy, this is not specific to conservative forces. Non-conservative forces can also do work that changes kinetic energy.
- **Result**: Option B is incorrect.

4. **Analyzing Option C**:
The statement suggests that a conservative force does not obey Newton's second law.
- **Conclusion**: This is false. Conservative forces can and do obey Newton's second law.
- **Result**: Option C is incorrect.

5. **Analyzing Option D**:
The statement indicates that the work done by the force depends only on the endpoints of the motion and not on the path taken.
- **Conclusion**: This is the defining characteristic of conservative forces. The work done by a conservative force is indeed dependent only on the initial and final positions, not the path taken.
- **Result**: Option D is correct.

### Final Answer:
The correct options are A and D.