The gravitational potential energy of a body depends on...

Question

The gravitational potential energy of a body:

1) depends on the fluid that surrounds the body

2) does not depend on the mass of the body

3) depends on the body temperature

4) depends on the chosen reference system

5) does not depend on the chosen reference system

I would like to know how, the 4th answer is correct and not the 2nd

That's what i thought in 1st place --> (P.E: M x G x H)

P.E = potential energy

M = Mass

H = Height

G = Gravity (10m/s)

Answer 1

When answering questions about potential energy, it's important to remember that the concept only really makes sense for comparison - the difference in potential associated with a change in the system's state. The reason it's called potential energy in the first place is because it's thought of as having the potential to be converted into some other kind of energy, whether that be a different form of stored potential energy or kinetic energy (motion).

Thus, we can't speak of the gravitational potential energy without setting a reference frame by which to compare one state to another. Wherever an object might currently be in a gravitational field, we are free to set that as its "home" location (with PE = 0), and then moving against the direction of the field (i.e. upward, on earth) would result in a positive change in potential energy, because allowing the object to fall back down would give it kinetic energy due to the acceleration of gravity. However, if we were instead to take that higher position as "home", then the assigned gravitational potential energy there would be zero, and the potential energy at the previous, lower location would be negative.

One way of making sense of this is in terms of work - moving from lower to higher potential energy requires work to be done to the object, such as the work your body would do to a barbell by lifting it off the ground. The work you do to the barbell is an energy input equal to the difference in PE values. In the symmetrical situation of lowering it back down, the barbell is instead doing work on you - an energy output of the same magnitude. When being raised, the barbell undergoes a positive change in PE due to energy input, and when pulling your arms back down to the ground, it undergoes negative change in PE due to energy output.

You may notice that the above discussion of PE change due to work never relies on actually setting a value for the PE in either the raised or lowered position. We could set either as our "home" location - or, if e.g. this was happening on a rooftop, we could set the ground level as "home", and both PE values would be positive, but still separated by the same difference.