If height doubles, gravitational potential energy relative to the ground changes by what factor?

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Multiple Choice

If height doubles, gravitational potential energy relative to the ground changes by what factor?

Explanation:
Gravitational potential energy near Earth’s surface scales linearly with height: PE = m g h. If you double the height, you replace h with 2h, giving PE' = m g (2h) = 2 m g h, which is twice the original energy. This assumes mass and the gravitational field strength g stay constant. So the potential energy doubles when height doubles. The other options would require different changes in height or different g/mass values, which aren’t the scenario here.

Gravitational potential energy near Earth’s surface scales linearly with height: PE = m g h. If you double the height, you replace h with 2h, giving PE' = m g (2h) = 2 m g h, which is twice the original energy. This assumes mass and the gravitational field strength g stay constant. So the potential energy doubles when height doubles. The other options would require different changes in height or different g/mass values, which aren’t the scenario here.

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