Show that the gravitational field intensity of the earth at any point is equal to the acceleration produced in the freely falling body at that point

The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocity along any desired trajectory. It tends toward center of the earth through its own acceleration, with gravitational pull due to earth acting over it.

When an object is dropped from rest and allowed to fall freely, it accelerates toward the Earth at a rate constant near the surface. The rate is determined by the mass of the Earth and the distance from its center. The gravitational field intensity at that point can be thought of as the gravitational force exerted on the object divided by its mass. Since the force causing the acceleration is the weight of the object, the gravitational field intensity directly relates to how quickly the object accelerates as it falls.

The intensity of gravitational field at any point in Earth is given by acceleration experienced by any freely falling body. In this context, it proves that this strength of gravitational field is indeed what causes an object to fall with acceleration so as to bring out the relation between intensity of gravitational field and the motion of falling bodies directly.