Question

A simple model consider a continent as a block (density $=2800kg/m^3$).
Floating in the mantle rock around it (density $=3300kg/m^3$). Assuming the continent is $35km$ thick (the averagr thickness of the Earth's crust), estimate the height of the continent above the surrounding rock.

Answer 1

Now, the weight of the continent and the force under the continent should be same.

Now, Force, $F=PA$

where $P=$ pressure and $A=$ area of the continent

Now, $P=h{\rho }_{r}g$

where $h$ is the height of continent in the mantle rock and ${\rho }_r$ is the density of mantle rock

Now, Weight of continent,$W=mg=V{\rho }_{c}g=HA{\rho }_{c}g$

where ${\rho }_c$ is the density of continent $H$ is the total height of continent

Now,

$F=W$

$or,h{\rho }_{r}g\times A=HA{\rho }_{c}g$

$or,h=\frac{H{\rho }_c}{{\rho }_r}=\frac{35\times 2800}{3300}km\approx 29.69km$

So, height of the continent above the surrounding rock $=(35-29.69)km=5.31km$