Respuesta :
Answer:
Option 4
Explanation:
As per the question:
Surface elevation above sea level = 4 km
Density of the crust = 2.7 [tex]gm/cm^{3}[/tex]
Density of the mantle = 3.4 g/cm^{3}
Now,
The elevation of the mountain range should be supported by the mantle and the crust with variable densities. The mountain roots in the mantle balances the height above the crust:
The depth of the mountain root is given by:
The depth of the root is given by:
Depth = [tex]\frac{Rock\ density\times sea\ level\ elevation}{density\ of\ mantle - density\ of\ crust}[/tex]
Depth = [tex]\frac{2.7\times 4}{3.4 - 2.7} = 15.43 km[/tex]
The root depth when there is a variation in the elevation to 1 km:
Depth = [tex]\frac{2.7\times 1}{3.4 - 2.7} = 3.86 km[/tex]
Hence, in order to support 1km elevation, erosion as:
Erosion = Mountain Height + Mountain Root = 15.4 + 4 = 19.5 km ≈ 20 km
