Can anyone Explain why a glass tips over when pushed from the top?

[linuxux]

1. The problem statement, all variables and given/known data

A glass has a height of 10 cm, and a diameter of 2 cm, it weight 300g and a coefficient of friction equal to .30 exists. Will it slip or tip?

2. Relevant equations

???

3. The attempt at a solution

Im almost certain there are no calculations informed since i have been hard pressed to find equations relating height and friction. But i did test this theory my self on a glass and it did tip. Is the reason it tips because the farther away you are from the base, the more perpendicular is the applied force in respect to the base, because is you push from the bottom of the glass all the force is against the friction. Is this right?

[Doc Al]

Is the reason it tips because the farther away you are from the base, the more perpendicular is the applied force in respect to the base, because is you push from the bottom of the glass all the force is against the friction. Is this right?
It's certainly true that the higher up the force is applied, the more torque it exerts. Whether it tips or not depends on whether the applied torque is greater than the torque due to gravity.

Assume for the moment that the glass doesn't slip. What applied force is required to overcome gravity? Would a force of that magnitude be enough to overcome static friction?