In the absence of air resistance, both a small object and a large object will accelerate at the same rate when dropped from the same height. This phenomenon is known as the equivalence principle and is a fundamental principle in physics.
According to the equivalence principle, the acceleration due to gravity is the same for all objects, regardless of their mass or composition. This acceleration is approximately 9.8 m/s² near the surface of the Earth and is denoted by the symbol 'g'. This means that every object, regardless of its size or mass, will experience the same acceleration due to gravity.
The reason for this equality in acceleration is that the force of gravity acting on an object is proportional to its mass, as described by Newton's second law of motion (F = ma). Consequently, when the mass of an object increases, the gravitational force acting on it also increases proportionally. As a result, the object's acceleration remains constant, and both small and large objects fall at the same rate.
It is worth noting that in real-world scenarios with air resistance or other external factors, the motion of objects may deviate from the idealized case. However, in the absence of such influences, the equivalence principle holds true, and objects of different sizes will accelerate at the same rate when dropped from the same height.