Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is 3×108 Nm-3 and its density is 3×103kg m-3. (Take g = 10 ms-2)
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a
4 km
b
8 km
c
10 km
d
16 km
answer is C.
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Detailed Solution
For a mountain of height h and base area A, weightW = AhρgSo, pressure at the base due to its own weight isP = WA = AhρgA = hρgThe mountain will exist, ifhρg≤Breaking stressh≤Breaking stressρgh≤30×1073×103×10= 104m = 10 km∴ hmax = 10 km