Help with free fall and Newtons second law problem

[Frankenstein19]

Homework Statement

Using Newtons second law, if an object with mass M is free falling (the only F acting upon it is its own weight), calculate the object's acceleration. What would happen to its acceleration should its mass duplicate?

Homework Equations

F=ma

The Attempt at a Solution

So since the object is free falling its acceleration is = to g. And that should be my answer right?
Could I just do
F=mg
mg=ma
g=a?
or is that just wrong?

then if the objects mass duplicates its acceleration stays the same because its constant? so the objects mass is irrelevant to its acceleration, right??

 

[cnh1995]

so the objects mass is irrelevant to its acceleration, right??

Right! If I remember correctly, that's exactly what Galileo proved by dropping two different masses from the Tower of Pisa..