(A) : There are some passengers in a stastionary compartment. A physical fight takes place between them because of different opinions. The position of c.m of system will not change.
(R ) : The fight between passengers is internal force.

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true but (R ) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze the assertion and reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that in a stationary compartment, if a physical fight occurs among passengers, the position of the center of mass (c.m) of the system will not change.
- A stationary compartment means that it is not moving with respect to an external observer.

2. **Defining the System**:
- We consider the compartment and the passengers inside it as a single system.
- The center of mass of a system is influenced by external forces acting on it.

3. **Identifying Forces**:
- The fight among the passengers involves internal forces. Internal forces are those forces that the particles of the system exert on each other.
- In this case, the forces exerted by the passengers during the fight are internal forces.

4. **Applying the Principle of Conservation of Momentum**:
- According to the principle of conservation of momentum, if no external force acts on a system, the total momentum of the system remains constant.
- Since the compartment is stationary and the net external force is zero, the momentum of the system (compartment + passengers) remains unchanged.

5. **Conclusion on Center of Mass**:
- Since the internal forces do not affect the motion of the center of mass, the position of the center of mass of the system will not change during the fight.
- Therefore, the assertion is true.

6. **Understanding the Reason**:
- The reason states that the fight between passengers is an internal force.
- This is also true, as the forces involved in the fight are between the passengers and do not involve any external influence.

7. **Relationship Between Assertion and Reason**:
- The reason correctly explains the assertion. Since the fight involves internal forces, the center of mass remains unchanged.

### Final Conclusion:
- Both the assertion and reason are true, and the reason is a correct explanation for the assertion.

### Answer:
- Both assertion (A) and reason (R) are true, and R is the correct explanation for A.

---