Question

Two rocks of identical mass sit high above the river. One rock is 10 meters above the river, and the other is 20 meters above the river. Which rock has the greatest potential energy?

Answer 1

Gravitational potential energy is greater for the rock
`20\; {\rm m}` above the river.

Step-by-step explanation:

The gravitational field near the surface of the earth is approximately uniform. Let
`g` denote the strength of the gravitational field near the surface of the earth.

Let
`m` denote the mass of each rock. Assume that the gravitational potential energy of the two rocks is
`0` when the rocks are at the surface of the river.

When the rock is at a height of
`h` above the river, the gravitational potential energy (
`\text{GPE}`) of that rock would be
`\text{GPE} = m\, g\, h`. In other words, the
`\text{GPE}\!` of the rock is proportional to its height relative to the ground.

Hence, among the two rocks,
`\text{GPE}` would be greater for the rock that is higher above the ground (
`20\; {\rm m}`) than the rock
`10\; {\rm m}` above the ground.