What are the kinds of plant geotropisms? Why do the root and the stem present opposite geotropisms?

The kinds of geotropisms are the positive geotropism, that in which the plant grows in favor of the gravitational force, as for instance, in roots and the negative geotropism, that against the gravitational force, for instance, in the stem.

Stem geotropism and Root geotropism are opposed due to different sensitivities to auxin concentration in these structures. The following experiment able to demonstrate the phenomenon: root and Stem are placed in a horizontal position (parallel to the ground) and naturally auxins concentrate along their bottom part.

Under this situation it is observed that the root grows downwards and the stem grows upwards. This happens due to, in the stem the high auxin concentration in the bottom makes this side grow (longitudinally) more and the structures arcs upwards and In the root the high auxin concentration in the bottom inhibits the growth of this side and the upper side grows more making the root to curve downwards.