Which of the following statement (S) is/are correct ?

Options

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

Answer

To determine which of the statements is correct regarding the work done by internal forces in a system, we need to analyze the statements based on the principles of work and energy in physics.

### Step-by-Step Solution:

1. **Understanding Internal Forces**:
Internal forces are forces that the objects within a system exert on each other. For example, in a system of two blocks connected by a spring, the force exerted by the spring on each block is an internal force.

2. **Work Done by Internal Forces**:
The work done by internal forces on a system can be defined as the sum of the work done by all internal forces acting on the particles of the system.

3. **Total Work Done by Internal Forces**:
- The total work done by internal forces is often zero when considering the entire system. This is because internal forces do not change the total energy of the system; they merely convert energy from one form to another within the system.
- For example, if one part of the system does work on another part, the energy transferred is balanced out by an equal and opposite work done by the second part on the first.

4. **Analyzing the Statements**:
- If the statement claims that the total work done by internal forces is sometimes zero, this is correct. This occurs in a closed system where internal forces do not result in a net change in the system's energy.
- If the statement also mentions that internal forces are equal in magnitude and opposite in direction, this is true according to Newton's third law of motion.

5. **Conclusion**:
Based on the analysis, we can conclude that the statement regarding internal forces and their work done can be correct under certain conditions.

### Final Answer:
The correct statement(s) regarding the work done by internal forces in a system is/are those that indicate that the total work done can sometimes be zero.