Final answer:
The change in gravitational potential energy of the center of mass of the rod can be calculated using the formula ΔPEg = mgh, where m is the mass of the rod, g is the acceleration due to gravity, and h is the change in height.
Step-by-step explanation:
The change in gravitational potential energy of an object is found by multiplying the mass of the object, the acceleration due to gravity, and the change in height; this is based on the conservation of energy where potential energy can be converted to other forms of energy, such as kinetic energy.
For example, if the initial height of the center of mass is h₁ and the final height is h₂, then the change in gravitational potential energy is ΔPEg = mg(h₂ - h₁).
It's important to note that gravitational potential energy is positive when the final height is greater than the initial height, and negative when the final height is less than the initial height.