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 of marking the correct statements regarding work done by internal forces, we will analyze each statement step-by-step.

### Step 1: Analyze Statement 1
**Statement 1:** The total work done by internal forces of a system on the system is always zero.

- **Analysis:** This statement is incorrect. Internal forces can do work on the system. For example, if we consider two charged particles, they exert forces on each other. If they move, the work done by these internal forces can be non-zero depending on their displacements. Therefore, this statement is **false**.

### Step 2: Analyze Statement 2
**Statement 2:** The total work done by internal forces of a system on the system is sometimes zero.

- **Analysis:** This statement is correct. For example, consider two blocks connected by a frictional force. The frictional forces act in opposite directions on the two blocks. If both blocks have the same mass and move the same distance, the work done by the frictional forces will cancel each other out, resulting in a total work done of zero. Thus, this statement is **true**.

### Step 3: Analyze Statement 3
**Statement 3:** The total work done by internal forces acting between the particles of a rigid body is always zero.

- **Analysis:** This statement is also correct. In a rigid body, the particles maintain fixed distances from each other. Therefore, there is no relative displacement between them, which means that the work done by internal forces (which depend on displacement) is zero. Thus, this statement is **true**.

### Step 4: Analyze Statement 4
**Statement 4:** The total work done by internal forces acting between the particles of a rigid body is sometimes zero.

- **Analysis:** This statement is incorrect. Since the relative displacement between particles in a rigid body is always zero, the work done by internal forces is always zero. Thus, this statement is **false**.

### Conclusion
After analyzing all statements:
- **Correct Statements:** Statement 2 and Statement 3.
- **Incorrect Statements:** Statement 1 and Statement 4.

### Final Answer
The correct statements are **B and C**.

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