Force on an object of mass m falling freely under gravitation by the earth is given by Universal Law of Gravitation:

F = or, F m

Now, clearly from above we can see that F depends on mass of the object.

Since, M = Mass of earth

r = Radius of earth

G = Nm²kg^-2 are constants

If g is the acceleration due to gravity on an object of mass m then,

F = m × g

Or, g =

Or, g =

Thus, g is independent of mass of the object.

Now, let two objects A of mass and B of mass fall from height h such that

Now, using the following equation of motion,

Here, u = 0, s = h and a = g

So,

Or,

Now, from above, since time depends on both h and g, which are both independent of masses, so both A and B come down at same time.