Question

Assuming that shear stress of base of a mountain is equal to force per unit area due to its weight, calcualte the maximum possible height(in $\text{km}$) of a mountain on the earth, if breaking stress of a typical rock is $3\times {10}^8{\text{Nm}}^{-2}$ and specific gravity is $3$.

Answer 1

Pressure due to self weight at base of the mountain
$p=\frac{W}{A}=h\rho g\le$Breaking stress
$h\le \frac{\text{Breaking stress}}{\rho g}=\frac{3\times {10}^8}{3\times {10}^3\times 10}$
$h\le 10$ km.