Question

If a mountain range has a crust that is 60 km thick and a surface elevation of 4 km above sea level, how much erosion is necessary to reduce the surface elevation to approximately one kilometer above sea level? (1) 5-6 km (2) 10-12 km (3) 15-18 km (4) 20-24 km (5) 25-30 km

Answer 1

Option 4

Step-by-step explanation:

As per the question:

Surface elevation above sea level = 4 km

Density of the crust = 2.7
`gm/cm^(3)`

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 =
`(Rock\ density* sea\ level\ elevation)/(density\ of\ mantle - density\ of\ crust)`

Depth =
`(2.7* 4)/(3.4 - 2.7) = 15.43 km`

The root depth when there is a variation in the elevation to 1 km:

Depth =
`(2.7* 1)/(3.4 - 2.7) = 3.86 km`

Hence, in order to support 1km elevation, erosion as:

Erosion = Mountain Height + Mountain Root = 15.4 + 4 = 19.5 km ≈ 20 km