Question

Why do stem and root show unilateral growth towards light and gravity of earth respectively?

Answer 1

Roots show positive gravitropism that is roots bend in response to gravity. This occurs due to plant hormone auxin. The polar transport of auxin from shoot tip to the roots inhibits cell expansion. So increase in concentration of auxin towards the root side causes differential growth resulting in root curvature towards gravity.
In case of stems, in the presence of asymmetric light, auxin will move towards the shaded side and will promote elongation of the cells on that side and this will cause curvature of plant towards the light source(positive phototropism).