The velocity of centre of mass of the system remains constant, if the total external force acting on the system is.

Options

A. a. minimum
B. b. maximum
C. c. unity
D. d. zero

Explanation

To solve the question, we need to analyze the relationship between the velocity of the center of mass, acceleration, and external forces acting on a system.

### Step-by-Step Solution:

1. **Understanding the Concept of Center of Mass (COM)**:
- The center of mass of a system is a point that represents the average position of all the mass in the system. The motion of the center of mass can be described by its velocity.

2. **Given Condition**:
- The problem states that the velocity of the center of mass remains constant. This is a key point because it implies that there is no change in the velocity over time.

3. **Implication of Constant Velocity**:
- If the velocity of the center of mass is constant, it means that the acceleration of the center of mass is zero. Mathematically, we can express this as:
\[ a_{COM} = 0 \]

4. **Relation Between Acceleration and Force**:
- According to Newton's second law, the net external force acting on a system is related to its acceleration:
\[ F_{net} = m \cdot a_{COM} \]
- Since we have established that \( a_{COM} = 0 \), we can substitute this into the equation:
\[ F_{net} = m \cdot 0 = 0 \]

5. **Conclusion**:
- Therefore, if the velocity of the center of mass remains constant, the net external force acting on the system must be zero. This leads us to conclude that:
\[ F_{net} = 0 \]

6. **Final Answer**:
- The total external force acting on the system is **zero**.