Which formula represents potential energy (PE) in relation to gravitational influence?

The formula that correctly represents potential energy (PE) due to gravitational influence is mgh. This formula reflects the energy an object possesses because of its position in a gravitational field.

In the expression, "m" stands for mass, "g" represents the acceleration due to gravity (approximately 9.81 m/s² on Earth), and "h" is the height of the object above a reference point, usually the ground, where the potential energy is considered to be zero. Therefore, the potential energy increases linearly with both the height of the object and its mass; as either of these values increases, the potential energy of the object in a gravitational field increases as well.

The other formulas listed are related to kinetic energy or force. Kinetic energy, which is energy of motion, is represented by 1/2mv^2 and mv^2/2, reflecting how mass and velocity work together in dynamic situations rather than positions under gravity. The formula mg, while related to weight (force due to gravity), does not incorporate height and thus cannot express potential energy directly.