Mark the correct statement(s).

Options

A. (a) Total work done by internal forces of a system on the system is always zero.
B. (b) Total work done by internal forces of a system on the system is sometimes zero.
C. (c) Total work done by internal forces acting between the particles of a rigid body is always zero.
D. (d) Total work done by internal forces acting between the particles of a rigid body is sometimes zero.

Explanation

To solve the question regarding the correctness of the statements about internal forces and work done, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Internal Forces**:
Internal forces are the forces that particles within a system exert on each other. For example, in a rigid body, the forces between the particles are internal forces.

2. **Analyzing Statement 1**:
- **Statement**: "Total work done by internal forces of a system on a system is always zero."
- **Analysis**: This statement is correct. The reason is that internal forces always act in pairs (Newton's third law), and thus the total work done by these forces cancels out, resulting in zero net work.

3. **Analyzing Statement 2**:
- **Statement**: "Total work done by internal forces of a system on the system is sometimes zero."
- **Analysis**: This statement is incorrect. As established in the analysis of Statement 1, the total work done by internal forces is always zero, not sometimes.

4. **Analyzing Statement 3**:
- **Statement**: "Total work done by internal forces between the particles of a rigid body is always zero."
- **Analysis**: This statement is also incorrect. While internal forces can balance each other, it does not mean that the total work done is always zero in every scenario, especially when considering the motion of the entire rigid body.

5. **Analyzing Statement 4**:
- **Statement**: "Total work done by internal forces acting between particles of a rigid body is sometimes zero."
- **Analysis**: This statement is misleading. The work done can be zero in certain configurations but is not guaranteed to be sometimes zero in all cases. Thus, this statement is also incorrect.

### Conclusion:
After analyzing all the statements, we find that only Statement 1 is correct. Therefore, the correct answer is:

**Correct Statement(s)**:
- Statement 1 is correct.