That's the joke/trick, it's basically begging the question. You can out a cheater by asking a question of the form:

Which is true, (A and A->B) or (A and A->C)?

A cheater will fret over whether B or C is true, while someone who did the work will probably immediately identify that A is false and that the question is misleadingly worded.

g is not a constant. It’s the measured acceleration at sea level on earth. Travel into orbit or to another planet and g will be different. The proper equation is:

F = GmM/r^2

Where m and M are the masses of the object and earth respectively, G is Newton’s universal gravitational constant, and r is the distance between the centre of masses of the object and earth. So why is there no mass in your little g? Because the force is directly proportional to the mass of the object (holding earth’s mass constant and the distance from it constant).