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Assuming that shear stress at the base o...

Assuming that shear stress at the base of a momuntain 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 strees of a typical rock is `33xx10^(8)N m^(-2)` and its density is `3xx10^(3) kg m^(-3)`.
(Take `g= 10 m s^(-2)`)

Text Solution

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For a mountain of heighth and base area A, weight `W= Ah rhog`. So pressure at the base due to its own weight will be `p=(W)/(A)=h rhog` The mountain will exist if, `h rho g lt` Breaking shear stress
`i.e, h=(30xx10^(7))/(3xx10^(3)xx10) (or) (h)_(max)=10 km` which is nearly the height of Mount Everest.
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