What is the relationship between loss in gravitational potential energy and work done against resistive forces?

The correct answer is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. When an object loses gravitational potential energy, that energy is converted into other forms, such as kinetic energy or work done against resistive forces.

In the scenario described, when an object moves downward in a gravitational field, it loses gravitational potential energy as it falls. This lost energy can either transform into kinetic energy, resulting in the object speeding up, or it can be used to do work against resistive forces such as friction or air resistance.

Thus, the total loss in gravitational potential energy is equal to the sum of the gain in kinetic energy and the work done against resistive forces. This relationship is fundamental in physics, particularly when analyzing motion in gravitational fields and other energy transfer processes.

In contrast, the other options do not accurately depict the relationship between the energy forms. The loss in potential energy does not equate solely to the gain in potential energy (as energy is conserved but transformed), kinetic energy alone does not account for resistive work, and resistive forces on their own do not encompass the entirety of energy transformation involved in the process.