Q134 / 160 · AP EAMCET 2023 (15 May Shift 1) · Physics

The maximum possible height of a mountain on earth is approximately (elastic limit of mountain rock $=30 \times 10^7 \mathrm{Nm}^{-2}$, average density of mountain rock $=3 \times 10^3 \mathrm{kgm}^{-3}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$ )

  • A
    $9 \mathrm{~km}$
  • Correct answer
    B
    $10 \mathrm{~km}$
  • C
    $12 \mathrm{~km}$
  • D
    $8.8 \mathrm{~km}$

Solution

$\begin{aligned} & \text { Elastic limit }=\mathrm{h} \rho \mathrm{g} \therefore \text { Height, } \mathrm{h}=\frac{\text { Elastic limit }}{\rho \mathrm{g}} \\ & \therefore \mathrm{h}=\frac{30 \times 10^7}{3 \times 10^3 \times 10}=10,000 \mathrm{~m}=10 \mathrm{~km}\end{aligned}$

Hence, the correct answer is option: 'B'.

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