Gravitational potential energy  |  ProblemWhich of the following statements are true regarding the gravitational potential energy of an object and how that energy changes when the object's vertical position changes? Group of answer choicesThe gravitational potential energy depends on the chosen vertical origin.The gravitational potential energy does not depend on the chosen vertical origin.The change in gravitational potential energy depends on the chosen vertical origin.The change in gravitational potential energy does not depend on the chosen vertical origin.

The gravitational potential energy of an object is given by the equation U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground.

1. The gravitational potential energy depends on the chosen vertical origin. True. The height (h) in the equation is measured from a reference point, often chosen to be the ground. If you change this reference point (i.e., change the vertical origin), the calculated gravitational potential energy will change.

2. The gravitational potential energy does not depend on the chosen vertical origin. False. As explained above, the gravitational potential energy does depend on the chosen vertical origin.

3. The change in gravitational potential energy depends on the chosen vertical origin. False. The change in gravitational potential energy depends only on the initial and final positions of the object, not on the chosen vertical origin. It is calculated as ΔU = mgΔh, where Δh is the change in height. This change in height is the same regardless of where you choose your vertical origin.

4. The change in gravitational potential energy does not depend on the chosen vertical origin. True. As explained above, the change in gravitational potential energy depends only on the change in height, not on the chosen vertical origin.