Question

3.
If the elastic limit of a typical rock is 3 x 108 Nm- and its mean density 3 10 kgm", estimate the
maximum height of a mountain on earth. Take g as 10 ms2​

Answer 1

Well, the pressure exerted by the mountain of height $\displaystyle\sf{h}$ and density $\displaystyle\sf{\rho}$ on the earth is given by,

$\displaystyle\longrightarrow\sf{P=\rho gh}$

The expression is similar to the hydrostatic pressure, right?!

The pressure is equal to nothing but its elastic limit. Thus,

$\displaystyle\longrightarrow\sf{P=3\times10^8\ N\ m}$

$\displaystyle\longrightarrow\sf{\rho=3\times10^3\ kg\ m^{-3}}$

$\displaystyle\longrightarrow\sf{g=10\ m\ s^{-2}}$

Then,

$\displaystyle\longrightarrow\sf{h=\dfrac{P}{\rho g}}$

$\displaystyle\longrightarrow\sf{h=\dfrac{3\times10^8}{3\times10^3\times10}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{h=10\ km}}}$