Final answer:
All objects, regardless of their mass, accelerate at the same rate (approximately 9.8 m/s²) toward the center of Earth when there is no air resistance or friction, due to the nature of gravitational acceleration where the mass of the object cancels out in the equation.
Step-by-step explanation:
When different objects fall at the same location on Earth, if air resistance and friction are negligible, they all experience the same rate of acceleration toward the center of Earth, regardless of their masses. This means that the correct answer to the student's question is C) Objects with different masses accelerate at the same rate. According to Newton's second law of motion, which relates force, mass, and acceleration, the acceleration (a) of an object is directly proportional to the net force acting on it and inversely proportional to its mass (a = F/m). However, gravitational acceleration is unique because the force of gravity on an object is directly proportional to its mass, which means that when calculating the acceleration due to gravity, the mass of the object cancels out, resulting in all objects falling with the same acceleration, which is approximately 9.8 m/s² on Earth's surface.
This phenomenon was demonstrated by Galileo Galilei and contradicted the commonly held belief that heavier objects fall faster than lighter ones. Factors such as air resistance can affect the rate at which objects fall, with objects having larger surface areas or less mass experiencing more resistance and potentially falling slower, but this is not due to a difference in gravitational acceleration. In conclusion, the relationship between the mass of the objects and the rate of acceleration they experience due to gravity is that there is no relationship: all objects in free fall accelerate at the same rate when not considering air resistance or friction.