I'm on a problem that can be simplified in the following way: 

> A box is placed on a horizontal plane, and is pinned to the ground on one side only such that it can tip over that side. Given a disturbance force normal to one of its side faces, how high does it need to be to make the box tip over? 

Diagram:
![enter image description here][1]

I think it is a very simple problem, and the way I see it the answer should be:
$$M(O) = y_F F-x_P P \Rightarrow F_{tipover}=\frac{x_P P}{y_F}$$

Which means that force does not depend on the height of the center of gravity. Someone insists the lower the CoG, the higher this force (the more stable the box). Intuitively it seems to make sense especially on an inclined plane, but the maths are against it at least on a horizontal plane.

What do you think? 

  [1]: https://i.sstatic.net/suUy9.png