The correct option is (c).
Explanation
Gravitational Potential Energy ($PE$) is the energy possessed by an object due to its position relative to the Earth's surface. The potential energy gained by an object of mass $m$ raised to a vertical height $h$ is mathematically expressed as:
$PE = mgh$
Where:
- $m$ = Mass of the object
- $g$ = Acceleration due to gravity
- $h$ = Vertical height
Statement-wise Analysis:
- Statement 1 is Incorrect: The gravitational potential energy depends on the mass of the object, not its volume. Two objects with the same volume but different densities (e.g., a plastic ball and a lead ball) will have different masses and, consequently, different potential energies. Therefore, volume is not a direct determinant.
- Statement 2 is Correct: As seen in the formula $PE = mgh$, the energy gained is directly proportional to the height ($h$) to which the object is raised. The higher the object, the greater the potential energy.
- Statement 3 is Correct: The potential energy depends on the acceleration due to gravity ($g$) at that specific location. Since $g$ varies slightly from place to place (e.g., poles vs. equator), the potential energy for the same mass and height will vary accordingly.
Key Takeaway:
Gravitational potential energy is strictly a function of mass, gravity, and height ($PE = mgh$). It is independent of the object's shape, size, or volume.