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Question: Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its ...

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 is3×108 N m−23 \times 10 ^ { 8 } \mathrm {~N} \mathrm {~m} ^ { - 2 } and its density is (Take

A

4 km

B

8 km

C

10 km

D

16 km

Answer

10 km

Explanation

Solution

: For a mountain of height h and base area A,

Weight

So, pressure at the base due to its own weight is

The mountain will exist, if

Breaking stress

h≤ Breaking stress ρgh \leq \frac { \text { Breaking stress } } { \rho g }

h≤30×1073×103×10=104 m=10Km\mathrm { h } \leq \frac { 30 \times 10 ^ { 7 } } { 3 \times 10 ^ { 3 } \times 10 } = 10 ^ { 4 } \mathrm {~m} = 10 \mathrm { Km }