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In analyzing certain geological features of the Earth, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep in the Earth, is the same over a large region and is equal to that exerted by the weight of the overlying material. That is, the pressure on the level of compensation is given by the hydrostatic (fluid) pressure formula. This requires, for example, that mountains have low-density roots; see Fig. 15-25. Consider a mountain 6.00 km high. The continental rocks have a density of 2.90 g/cm 3 ; beneath the continent is the mantle, with a density of 3.30 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 compensation will cancel out.)
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