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Assuming that shear stress at the base o...

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 `3xx10^8Nm^-3` and its density `3xx10^-3kgm^-3`. (Take `g=10ms^-2`)

A

5 km

B

6 km

C

8 km

D

10 km

Text Solution

Verified by Experts

The correct Answer is:
D
Suppose that the height of the mountain = h
and the density of the rock `= rho`
`:.` Force per unit area at the base
`= ("Weight")/("Area") = ("Volume" xx "density" xx g)/(A)`
or Pressure `= (A h rho g)/(A) = h rho g`
The material at the base experiences this pressure in the vertical direction. But the sides of the mountain are free to move outwars. Hence the mountain suffers a shearing stress of the order of `hrho g`.
`:.` The mountain will exist if `h rho g lt` Breaking shear stress
`:. h_("max") rho g = 3 xx 10^(8) N//m^(2)`
`:. h_("max") = (3 xx 10^(8))/(3 xx 10^(3) xx 10) = 10^(4) m = 10 km`
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