Objects of different masses fall to the ground at the same time in the absence of significant air resistance due to a fundamental principle in physics called the equivalence principle and the effect of gravity.
The equivalence principle, proposed by Albert Einstein, states that the effects of gravity are indistinguishable from the effects of acceleration. When objects fall near the surface of the Earth, they experience the force of gravity pulling them downward. According to the equivalence principle, this force of gravity is equivalent to an acceleration acting on the objects.
Now, when objects fall, the force of gravity accelerates them downward. The acceleration due to gravity near the surface of the Earth is approximately 9.8 meters per second squared (9.8 m/s^2). This means that every second an object is falling, its velocity increases by 9.8 meters per second.
The mass of an object is a measure of the amount of matter it contains, and it affects the force required to accelerate the object. A more massive object requires a larger force to accelerate it compared to a less massive object. However, the acceleration due to gravity is the same for all objects near the Earth's surface, regardless of their mass.
According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration. In the case of free-falling objects near the Earth's surface, the force of gravity acting on the objects is their mass multiplied by the acceleration due to gravity.
Since the acceleration due to gravity is the same for all objects, the force of gravity acting on them is proportional to their mass. Consequently, the more massive object experiences a larger gravitational force, but it also requires a larger force to accelerate it. These effects cancel each other out, resulting in both objects accelerating at the same rate.
As a result, objects of different masses fall to the ground at the same time when the effects of air resistance are negligible. This phenomenon was famously demonstrated by Galileo's experiments, and it has been verified through numerous experiments since then.