According to the work-energy theorem, what does the parallel gravitational force component multiplied by distance equal?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. When considering the parallel gravitational force component, it plays a crucial role in determining how much work is done when an object moves through a distance in the direction of that force, such as a ball rolling down a hill.

When you multiply the parallel component of the gravitational force by the distance over which it acts, you are calculating the work done by that gravitational force. This work is what contributes to the change in the object's kinetic energy. As the object moves down, the gravitational force causes it to accelerate, leading to an increase in its kinetic energy. Thus, the correct relationship highlighted by the work-energy theorem directly ties the parallel gravitational force's action to the resultant change in kinetic energy of the object involved.