Please explain how you do this and what equations you use. . A mountain range 4

Question

Please explain how you do this and what equations you use.

. A mountain range 4 km high is in Airy isostatic equilibrium. (10 points)

(a) During a period of erosion, a 2 km thickness of material is removed from the mountains. When the new isostatic equilibrium is achieved, how high are the mountains?

(b) How much material must be eroded to bring the mountains eventually down to the sea level? Use the crust and mantle densities of 2800 kg/m3 and 3300 km/m3, respectively.

C) How High would they be if 10km of material were eroded away?

Explanation / Answer

As per the Airy's hypothesis the ratio of densities of 0.8 which means out of total 10 parts the rock is 8 parts below the surface of ocean and 2 parts above.

Therefore 4 km high mountain means there's 16 kilometer rock beneath the spheriod of earth(sea level).

Now out of 4 km 2 km is removed so we have so we have a total of = 16+2 kilometer

= 18 kilometer

so 20% of this would be 3.6 kilometer.

Therfore mountains are now 3.6 kilometer high.

(b) Density ratio = (2800 )/(3300)

= 0.8484

But in order to bring the mountains eventually down to the sea level we need to have infinitesimal small amount of rock beneath the sea level there fore we need to practically remove all the material.

(c) Out of 20 km, 10km of material were eroded away: so we have now 10 kilometer of material:

Density ratio = 0.8484

so height above sea level = 10- (0.8484 x 10) = 1.5151km

Therefore new height above sea level is 1.5151km.

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