Limit of a mountain using universal gravitation

[BoldKnight399]

The height of a mountain is limited by the ability of the atoms at the bottom to sustain the weight of the materials above them. Assuming that the tallest mountains on Earth (at about 8850m) are near this limit, how tall could that mountain be on Mars, with mass .11Me and radius .53 Re?

I know that this should include the equation:
F=G(m1*m2/R^2) but I don't understand how. To be honest I don't understand how one could possibly find an actual number from this limited information. (it is a multiple choice answer question, and all the choices are numbers. However, I would rather solve it myself so I can understand the concept.)

 

[Redbelly98]

Hint: what would the value of g be on the surface of Mars?