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Explain why the maximum height of a mountain on earth is approximately 10km?

Explain why the maximum height of a mountain on earth is approximately 10km?
 

Grade:10

6 Answers

mahendra
83 Points
8 years ago
The maximum height of mountain on earth depends upon shear modulus of rock. At the
base of the mountain, the stress due to all the rock on the top should be less than the
critical shear stress at which the rock begins to flow. Suppose the height of the mountain
is h and the density of its rock is ρ . Then force per unit area (due to the weight of the
mountain) at the base = hρ g
The material at the experience this force per unit area in the vertical direction, but sides
of the mountain area free. Hence there is a tangential shear of the order of hρ g . The
elastic limit for a typical rock is about 3 ×108 Nm −2 and its density is 3 ×103 kgm −3
Hence hmax ρ g = 3 ×108
Or hmax
3 × 108
3 × 108
=
=
= 10, 000m = 10km
ρg
3 × 103 × 9.8
This is more than the height of the Mount Everest.
 
sathish
79 Points
8 years ago
The maximum height of mountain on earth depends upon shear modulus of rock. At thebase of the mountain, the stress due to all the rock on the top should be less than thecritical shear stress at which ...
salvathshaik
164 Points
8 years ago
The maximum height of mountain on earth depends upon shear modulus of rock. At thebase of the mountain, the stress due to all the rock on the top should be less than thecritical shear stress at which the rock begins to flow. Suppose the height of the mountainis h and the density of its rock is ρ . Then force per unit area (due to the weight of themountain) at the base = hρ gThe material at the experience this force per unit area in the vertical direction, but sidesof the mountain area free. Hence there is a tangential shear of the order of hρ g . Theelastic limit for a typical rock is about 3 ×108 Nm −2 and its density is 3 ×103 kgm −3Hence hmax ρ g = 3 ×108Or hmax3 × 1083 × 108=== 10, 000m = 10kmρg3 × 103 × 9.8This is more than the height of the Mount Everest.
Surendra
54 Points
8 years ago
The maximum height of mountain on earth depends upon shear modulus of rock. At thebase of the mountain, the stress due to all the rock on the top should be less than thecritical shear stress at which the rock begins to flow. Suppose the height of the mountainis h and the density of its rock is ρ . Then force per unit area (due to the weight of themountain) at the base = hρ gThe material at the experience this force per unit area in the vertical direction, but sidesof the mountain area free. Hence there is a tangential shear of the order of hρ g . Theelastic limit for a typical rock is about 3 ×108 Nm −2 and its density is 3 ×103 kgm −3Hence hmax ρ g = 3 ×108Or hmax3 × 1083 × 108=== 10, 000m = 10kmρg3 × 103 × 9.8This is more than the height of the Mount Everest.
Hello
13 Points
6 years ago
Max height hhhe.  Eee. See. Eee. Eeekkk. Sskkk.  Ssokskkk.  Ssjkkkske.  Sskkkkse. Kkkskks. Ssnkososos. Ssjjsjsjsns njjsnsjsjdj sjjsjsjsjs snsiheello njsnsnsnsnhello e. eejsjsnsh hi jsjsnsnnsns hello
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

The maximum height of mountain on earth depends upon shear modulus of rock.
At the base of the mountain, the stress due to all the rock on the top should be less than the critical shear stress at which the rock begins to flow.
Suppose the height of the mountain is h and the density of its rock is ρ .
Then force per unit area (due to the weight of the mountain) at the base = hρ g
The material at the experience this force per unit area in the vertical direction, but sides
of the mountain area free.
Hence there is a tangential shear of the order of hρ g .
The elastic limit for a typical rock is about 3 ×108 Nm −2
and its density is 3 ×103 kgm −3
Hence hmax ρ g = 3 ×108
Or hmax 3 × 10^8
3 × 10^8
= 10, 000m
= 10km
ρg
3 × 10^3 × 9.8
This is more than the height of the Mount Everest.

Thanks and Regards

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