Answer:
GE = ME - , which agrees with option C in your list.
Explanation:
The definition of Mechanical Energy (ME) of a system is the addition of the gravitational potential energy (GE) plus the kinetic energy (KE) of the system:
ME = GE + KE
Given that the KE is: ,
solving for GE in the formula above gives:
GE = ME - KE = ME - , which agrees with option C
From the gravity acceleration theorem due to a celestial body or planet, we have that the Force is given as
Where,
F = Strength
G = Universal acceleration constant
M = Mass of the planet
m = body mass
r = Distance between centers of gravity
The acceleration by gravity would be given under the relationship
Here the acceleration is independent of the mass of the body m. This is because the force itself depended on the mass of the object.
On the other hand, the acceleration of Newton's second law states that
Where the acceleration is inversely proportional to the mass but the Force does not depend explicitly on the mass of the object (Like the other case) and therefore the term of the mass must not necessarily be canceled but instead, considered.