Final answer:
The force of gravity acting on an object with mass m is given by the equation F = mg, where g is the constant acceleration due to gravity on Earth, approximately 9.80 m/s². Therefore, the correct answer is C. F = mg.
Step-by-step explanation:
The relationship between the force of gravity acting on an object (F) and its mass (m) in the absence of air resistance is given by the equation F = mg. This equation derives from Newton's second law of motion, which states that Fnet = ma, where Fnet is the net force on an object, m is its mass, and a is the acceleration. Since the only acceleration occurring is due to gravity (g), and assuming g is constant at about 9.80 m/s² on Earth, the force due to gravity is directly proportional to the mass. Therefore, the correct relationship is C. F = mg.