Question

Explain why the maximum height of mountain on earth is approximately 10 km?

Answer 1

maximum height of mountain depends on tangential or shearing 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.
Assume the height of the mountain is h and the density of its rock is $\rho$ then, stress { e.g., force per unit area} at the base = $h\rho g$
Where g is acceleration due to gravity .

The material at the base experiences 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 hρg . We also know, elastic limit for a typical rock is 3 × 10^8 N/m² , density of rock is 3 × 10³ kg/m³

so, 3 × 10^8 = $h_{max}$ × 3 × 10³ × 10
so, $h_{max}$ = 10⁴ m = 10km