Please Help and show steps In analyzing certain geological features, it is often

Question

Please Help and show steps

In analyzing certain geological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the overlying material. Thus, the pressure on the level of compensation is given by the fluid pressure formula. This model requires, for one thing , tht mountains have roots of continental rock extending into the denser mantle ( see figure 6 - next page ). Consider a mountain6.0 km high. The continental rocks have density of 2.9 g/cm 3. and beneath the continent the mantle has a density of 3.3 g/cm 3. Calculate the depth D of the root. {Hint: Set the pressure at points a and b equal; the depth y of the level of compression will cancel out.)

Explanation / Answer

Ignoring the air pressure...

We move top down till the point 'b'..

The total pressure is H1*density(continent)*g + H2*density(Mantle)*g

= 32*2.9*9.8+D*3.3*9.8.............(i)

Now, we go top down till 'a'

Total pressure = H3*density(continent)*g

=(38+D)*2.9*9,8............(ii)

Since pressure at 'a' and 'b' is same

equating (i) and (ii)

32*2.9 + 3.3D =38*2.9 + 2.9D

0.4D=6*2.9

D=43.5km

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