Question

The maximum possible height of a mountain on Earth is approximately.

• A. \( 9 \, \text{km} \)
• B. \( 10 \, \text{km} \)
• C. \( 12 \, \text{km} \)
• D. \( 8.8 \, \text{km} \)

Hint:

When calculating the height based on the elastic limit, ensure you correctly substitute the given values into the formula for material strength.

Answer 1

The Correct Option is B

To calculate the maximum height of the mountain, we can use the formula for the elastic limit of a material: \[ \sigma = \rho g h \] where: - \( \sigma \) is the elastic limit, - \( \rho \) is the density of the material, - \( g \) is the acceleration due to gravity, - \( h \) is the height. We are given: - \( \sigma = 30 \times 10^7 \, \text{N/m}^2 \), - \( \rho = 3 \times 10^3 \, \text{kg/m}^3 \), - \( g = 10 \, \text{m/s}^2 \). Substitute these values into the formula: \[ 30 \times 10^7 = 3 \times 10^3 \times 10 \times h \] Solving for \( h \): \[ h = \frac{30 \times 10^7}{3 \times 10^3 \times 10} = \frac{30 \times 10^7}{3 \times 10^4} = 10 \, \text{km} \] Therefore, the maximum possible height of a mountain is \( 10 \, \text{km} \).