Question

Where will the water to rise higher: in the capillaries of equal radius, at the foot of a high mountain or at its peak?

Answer 1

The height of the liquid in the capillary: h ∼ 2σ/ρRg.
At the top of the mountain free-fall acceleration is smaller than at the foot, that is why the height will be greater. The other parameters (surface tension, density, and radius) do not depend on the height.