Question

The height of a mountain is $ H $ and the density of its rock is $ 3 \times 10^{3} kg/m^{-3} $ . If the elastic limit of the rock is $ 3 \times 10^{8} N/m^{-2} $ , find the height of the mountain

• A. 50 km
• B. 30 km
• C. 8 km
• D. 10 km

Answer 1

Answer: (D)

Stress $=\frac{F}{A}$
$=\frac{mg}{A}=\frac{Vdg}{A}=\frac{AHdg}{A}=Hdg$
Elastic limit of the rock $=3\times 10^{8} N/m^{2}$
$3\times 10^{8}=Hdg$
$3 \times 10^{8}=H \times 3\times 10^{4}$
$\Rightarrow H=10\,km$