Question

Why the maximum height of a mountain on Earth is ~10km?

Answer 1

The maximum height of mountain on earth depends upon shear modulus of rock. At the
base of the mountain, the stress due to all the rock on the top should be less than the
critical shear stress at which the rock begins to flow. Suppose the height of the mountain
is h and the density of its rock is ρ . Then force per unit area (due to the weight of the
mountain) at the base = hρ g
The material at the experience this force per unit area in the vertical direction, but sides
of the mountain area free. Hence there is a tangential shear of the order of hρ g . The
elastic limit for a typical rock is about 3 ×108 Nm −2 and its density is 3 ×103 kgm −3
Hence hmax ρ g = 3 ×108
Or hmax
3 × 108
3 × 108
=
=
= 10, 000m = 10km
ρg
3 × 103 × 9.8
This is more than the height of the Mount Everest