Final answer:
The quantity (mg) in gravitational potential energy problems represents the weight of the object, not its mass, speed, or momentum.
Step-by-step explanation:
In gravitational potential energy problems, the quantity (mg) represents the weight of the object. When we lift an object against gravity, we must exert a force equivalent to its weight, which is the product of its mass (m) and the acceleration due to gravity (g). Therefore, lifting an object through a height (h) requires work equal to the force applied (which is the object's weight) times the distance (height) moved, thus W = mgh defines the gravitational potential energy (PEg) added to the system.