A man stands at one end of a boat which is stationary in water. Neglect water resistance. The man now moves to the other end of the boat and again becomes stationary. The centre of mass of the 'man plus boat' system will remain stationary with respect to water

Options

A. only when the man is stationary initially and finally
B. only if the man moves without acceleration on the boat
C. only if the man and the boat have equal masses
D. in all cases

Explanation

To solve the problem, we need to analyze the situation step by step, focusing on the concept of the center of mass and the effects of internal movements within a closed system.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a man and a boat, which together form a closed system. Initially, the boat is stationary in water, and we will assume the water is not providing any resistance.

2. **Initial Position**:
- The man stands at one end of the boat. At this point, the center of mass of the 'man plus boat' system is located at a certain position relative to the water.

3. **Movement of the Man**:
- The man moves to the other end of the boat. During this movement, he is not exerting any external force on the system (the boat and the water), as we are neglecting water resistance.

4. **Internal Forces**:
- The movement of the man causes the boat to shift slightly in the opposite direction due to the conservation of momentum. This is an example of internal forces acting within the system (the man pushing against the boat).

5. **Final Position**:
- Once the man reaches the other end of the boat and becomes stationary again, the system (man plus boat) will have a new configuration, but the total momentum of the system remains conserved.

6. **Center of Mass Calculation**:
- The center of mass of the system is calculated based on the positions and masses of the man and the boat. Since there are no external forces acting on the system, the center of mass will not change its position with respect to the water.

7. **Conclusion**:
- Therefore, the center of mass of the 'man plus boat' system remains stationary with respect to the water throughout the man's movement.

### Final Answer:
The center of mass of the 'man plus boat' system will remain stationary with respect to the water.

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