If a heavy box remains stationary despite a pushing force being applied, it implies that:

The correct option is

The force of static friction balances the applied force.

Explanation

This Newton's First Law of Motion and the concept of static friction. According to Newton's First Law, an object at rest will remain at rest unless acted upon by an unbalanced external force. If an object remains stationary despite an applied force, the net force acting on it must be zero.

Detailed Analysis:

• The applied force is zero. is Incorrect: The question explicitly states that a pushing force is being applied. Therefore, the applied force is non-zero.
• The force of static friction is greater than the applied force. is Incorrect: Friction is a passive, reactive force. It cannot exceed the applied force when the object is stationary. If static friction were greater than the applied force, the net force would be in the direction of friction, causing the box to accelerate backward, which violates physical laws.
• The force of static friction balances the applied force. is Correct: Static friction is a self-adjusting force. When an external force is applied to a stationary object, the force of static friction increases linearly to match the magnitude of the applied force, acting in the opposite direction. Since the box remains stationary (acceleration is zero), the forces must be in equilibrium. Therefore, the force of static friction exactly balances the applied force ($f_s = F_{applied}$).
• The inertia of the box is infinite. is Incorrect: Inertia is a measure of mass. While a heavy box has high inertia, it is not infinite. The box remains stationary not because inertia is infinite, but because the applied force has not yet exceeded the maximum limit of static friction (limiting friction).

Key Takeaway:

Static friction is a self-adjusting force that equals the applied external force in magnitude and acts in the opposite direction, provided the object remains at rest.