Which has more gravitational potential energy—a book sitting on a desk or the same
book sitting on the floor? Why?

The book sitting on the desk

Explanation:

The gravitational potential energy of an object is the energy possessed by the object due to its position relative to the ground.

It is calculated as:

where

m is the mass of the object

g is the acceleration due to gravity

h is the height of the object with respect to the ground

From the formula, we see that the GPE of an object is directly proportional to the heigth h: so, the higher the location of the object, the larger the GPE.

In this problem, we are comparing a book sitting on a desk and the same book sitting on the floor. In the two situations, the mass of the book is the same; however, in the first case, the value of the height is h, while in the second case, the value of h is lower (because the book is located at a lower height, being on the floor).

Therefore, we can conclude that the first book must have a larger GPE, since it has a larger value of h.