It doubles.
Explanation
Gravitational Potential Energy (GPE) is the energy possessed by an object due to its position relative to a gravitational source, typically the Earth. For objects near the Earth's surface, the potential energy is calculated using the formula:
$PE = mgh$
Where:
- $m$ is the mass of the object.
- $g$ is the acceleration due to gravity (approximately constant near the surface).
- $h$ is the height above the reference level (ground).
Analysis:
Since mass ($m$) and acceleration due to gravity ($g$) remain constant for a specific object near the surface, the gravitational potential energy is directly proportional to the height ($h$).
- Initial State: At height $h$, the potential energy is $PE_1 = mgh$.
- Final State: When the object is lifted to a height $2h$, the new potential energy becomes $PE_2 = mg(2h) = 2mgh$.
Comparing the two states, $PE_2 = 2 \times PE_1$. Therefore, the gravitational potential energy doubles.
Key Takeaway:
Gravitational potential energy is directly proportional to the vertical height ($PE \propto h$). Doubling the height results in a doubling of the potential energy, assuming mass and gravity remain constant.