Question

Free fall is a situation in which the only force acting upon an object is gravity. Why do all objects in free fall have the same acceleration?

Answer 1

free fall is a special type of motion in which the only force acting upon an object is gravity.  all objects will fall with the same rate of acceleration, regardless of their mass.

Answer 2

Answer:

The force of gravity between an object of mass m and Earth M at distance r is as follows (G is gravitational constant):

F = (G) x (m) x (M) / (r^2)

Now, we also know that a force acting on the object is F = (mass) x (acceleration).

Rewrite the first formula as:

F = (m) x (G x M / r^2)

The (G x M / r^2) part is precomputed for the near-surface of Earth and is referred to a gravitational acceleration g:

F = (m) x (g)

As you can see g (or G x M / r^2) does not depend on the mass of the object, only on the mass of Earth but that is the same for all objects in free fall (towards Earth).