Gravitational force does indeed act on all objects in proportion to their masses, as described by Newton’s law of universal gravitation. However, the key to understanding why heavier objects do not fall faster than lighter objects lies in the relationship between the gravitational force and the object’s inertia (its resistance to acceleration).
The force of gravity acting on an object is given by:
where m1 is the mass of the Earth and m2 is the mass of the falling object.
This force is responsible for accelerating the object downward. According to Newton’s second law of motion:
where m is the object’s mass and a is its acceleration. The acceleration a of an object due to gravity can be found by rearranging this equation:
Notice that the mass of the falling object, m2, cancels out, so the acceleration due to gravity a is independent of the object’s mass. This means that all objects, regardless of their mass, experience the same acceleration a=g, where g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
Therefore, both heavy and light objects fall at the same rate in the absence of air resistance. The heavier object does experience a greater gravitational force, but it also has more inertia, so it requires more force to achieve the same acceleration as the lighter object. This balance results in both objects falling at the same rate.
In real-world situations, air resistance can affect the falling speed of objects, and lighter objects may be more affected by air resistance than heavier ones, but in a vacuum (where air resistance is absent), all objects fall at the same rate.