Explanation
- 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 = 10, 000m = 10km
Hence , maximum height of mountain is 10km.