The applied force is balanced by opposing forces.
Explanation
According to Newton's Second Law of Motion, the net external force acting on an object is equal to the rate of change of its momentum ($F_{net} = \frac{dp}{dt}$). Therefore, a change in momentum occurs if and only if there is a non-zero net force. Conversely, if momentum is constant, the net force acting on the object must be zero.
Option Analysis
- The applied force is unbalanced. is incorrect: An unbalanced force implies a non-zero net force. This would cause acceleration and, consequently, a change in the object's momentum.
- The applied force is balanced by opposing forces. is correct: The momentum remains constant ($\Delta p = 0$). This implies that the net force on the object is zero. For the net force to be zero despite an applied force, there must be equal and opposite forces (such as friction or air resistance) balancing the applied force.
- The object has negligible mass. is incorrect: The mass of the object does not negate Newton's laws. Even an object with negligible mass would undergo a change in momentum if subjected to a net unbalanced force.
- The object is moving in a frictionless environment. is incorrect: In a frictionless environment, there are no resistive forces to oppose motion. Therefore, a single applied force would remain unbalanced, leading to continuous acceleration and a change in momentum.
Key Takeaway: Constant momentum implies zero acceleration. If an external force acts on a body without changing its momentum, the system is in dynamic equilibrium, meaning the applied force is perfectly balanced by opposing forces.