Final answer:
The statement that a system is in neutral equilibrium if its equilibrium is independent of displacements is true, exemplified by a marble on a flat surface that remains in equilibrium despite being moved.
Step-by-step explanation:
The statement that a system is in neutral equilibrium if its equilibrium is independent of displacements from its original position is indeed true. For example, we can consider a marble resting on a flat horizontal surface. If we move the marble to a new position on this flat surface, there is no net force pushing it back or away from this new position. This means that the marble is in neutral equilibrium because its state of equilibrium has not changed due to the displacement.
In contrast, a system in stable equilibrium will experience a restoring force or torque when displaced, which tends to return it to its original position. Conversely, a system in unstable equilibrium will experience a force or torque that moves it further away from equilibrium when displaced.
To further illustrate the concept, consider the marble on a saddle. For displacements toward the front or back, the marble is in stable equilibrium because the shape of the saddle will cause the marble to roll back to the middle. However, for displacements to the side, the marble is in unstable equilibrium because it will tend to roll away from the center. This example demonstrates the complexity of equilibrium types in various conditions.