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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

4 Km

B

8 Km

C

10 Km

D

16 Km

Text Solution

Verified by Experts

The correct Answer is:
C
For a mountain of height h and base area A, weight `W = Ahrhog`
So, pressure at the base sue to its own weight is `P = (W)/(A) = (Ahrhog)/(A) = hrhog`
The mountain will exist, if `hrhog le` Breaking stress `therefore h le ("Breaking stress")/(rhog)`
`h le (30xx 10^(7))/(3xx 10^(3) xx 10) = 10^(4) m = 10 Km`
`therefore h_("max") = 10 km`
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Knowledge Check

  • The breaking stress of a cylindrical rod is 10^(6) N//m^(2) . If the maximum possible height of the rod is 10 m, then the density of the material of the rod is [use g = 10m//s^(2) ]

    A
    `10^(3) kg//m^(3)`
    B
    `2 xx 10^(3) kg//m^(3)`
    C
    `10^(4) kg//m^(3)`
    D
    `2 xx 10^(4) kg//m^(3)`

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