Explanation:

When the external forces acting on a system have a zero resultant, it means that the vector sum of all the external forces is zero. In other words, the forces cancel each other out and there is no net force acting on the system.

Centre of Mass:

The centre of mass of a system is the point at which the entire mass of the system can be considered to be concentrated. It is the average position of all the particles that make up the system, weighted by their respective masses.

Effect of Zero Resultant External Forces:

When the external forces acting on a system have zero resultant, the following can be observed:

1. Centre of Mass Must Not Move:
Since there is no net force acting on the system, the centre of mass will not experience any external force to cause it to move. Therefore, the centre of mass must not move.

2. Centre of Mass May Move:
Although the centre of mass must not move due to zero resultant external forces, it is still possible for the centre of mass to move if there are internal forces acting within the system. Internal forces are forces between the particles within the system and do not affect the net force on the system as a whole.

3. Centre of Mass Must Not Accelerate:
Since there is no net force acting on the system, the centre of mass will not experience any external force to cause it to accelerate. Therefore, the centre of mass must not accelerate.

4. Centre of Mass May Accelerate:
Similar to the movement, the centre of mass may accelerate if there are internal forces acting within the system. Internal forces can cause the particles within the system to accelerate, which in turn can affect the acceleration of the centre of mass.

In conclusion, when the external forces acting on a system have zero resultant, the centre of mass must not move and must not accelerate. However, it is important to note that the centre of mass may move or accelerate if there are internal forces acting within the system.