Final answer:
If the height of an object from the ground is doubled, its gravitational potential energy (PEg) also doubles, since PEg is directly proportional to its height when mass and gravity remain constant.
Step-by-step explanation:
When considering what happens to PE of an object when its height from the ground doubles, we look at gravitational potential energy (PEg). The formula for gravitational potential energy is PEg = mgh, where m is mass, g is the acceleration due to gravity, and h is height. When the height h is doubled, the PEg doubles, assuming mass m and gravity g are constant. For instance, if an object at height h has a potential energy of X, then at a height of 2h, its potential energy will be 2X. The work done in lifting the object is equivalent to the gravitational potential energy gained by the object-earth system. Therefore, by doubling the height, you perform twice the work to achieve double the potential energy. If the height (
ℎ
h) of the object doubles, the gravitational potential energy will also double, assuming the mass (
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m) remains constant. This is because the gravitational potential energy is directly proportional to the height. Therefore, an increase in height results in a proportional increase in potential energy, and doubling the height will lead to a doubling of the potential energy.