Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is `3xx10^8Nm^-3` and its density `3xx10^-3kgm^-3`. (Take `g=10ms^-2`)

Options

A. `4km`
B. `8km`
C. `10km`
D. `16km`

Answer

C

Explanation

For a mountain of height `h` and base area A, weight `W=Ahrhog`
So, pressure at the base due to its own weight is
`P=(W)/(A)=(Ahrhog)/(A)=hrhog`
the mountain will exist, if
`hrhogle` breaking stress
`hle("breaking" stress)/(rhog)`
`hle(3010^7)/(3xx10^3xx10)=10^4m=10km`
`h_(max)=10km`