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MMLU-Pro / 10273 / A heavy object can sink into the ground during an earthquake if the shaking…

Problem

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question

A heavy object can sink into the ground during an earthquake if the shaking causes the ground to undergo liquefaction, in which the soil grains experience little friction as they slide over one another. The ground is then effectively quicksand. The possibility of liquefaction in sandy ground can be predicted in terms of the void ratio ee for a sample of the ground: e=Vvoids Vgrains . e=\frac{V_{\text {voids }}}{V_{\text {grains }}} . Here, Vgrains V_{\text {grains }} is the total volume of the sand grains in the sample and Vvoids V_{\text {voids }} is the total volume between the grains (in the voids). If ee exceeds a critical value of 0.80 , liquefaction can occur during an earthquake. What is the corresponding sand density ρsand \rho_{\text {sand }} ? Solid silicon dioxide (the primary component of sand) has a density of $\rho_{\mathrm{SiO}_2}=2.600 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$.
Plain-text mathematical notation (without MathML)
A heavy object can sink into the ground during an earthquake if the shaking causes the ground to undergo liquefaction, in which the soil grains experience little friction as they slide over one another. The ground is then effectively quicksand. The possibility of liquefaction in sandy ground can be predicted in terms of the void ratio e for a sample of the ground:
e=(V_(voids ))/(V_(grains )).
Here, V_(grains ) is the total volume of the sand grains in the sample and V_(voids ) is the total volume between the grains (in the voids). If e exceeds a critical value of 0.80 , liquefaction can occur during an earthquake. What is the corresponding sand density ρ_(sand ) ? Solid silicon dioxide (the primary component of sand) has a density of $\rho_{\mathrm{SiO}_2}=2.600 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$.
Original LaTeX notation
A heavy object can sink into the ground during an earthquake if the shaking causes the ground to undergo liquefaction, in which the soil grains experience little friction as they slide over one another. The ground is then effectively quicksand. The possibility of liquefaction in sandy ground can be predicted in terms of the void ratio $e$ for a sample of the ground:
$$
e=\frac{V_{\text {voids }}}{V_{\text {grains }}} .
$$
Here, $V_{\text {grains }}$ is the total volume of the sand grains in the sample and $V_{\text {voids }}$ is the total volume between the grains (in the voids). If $e$ exceeds a critical value of 0.80 , liquefaction can occur during an earthquake. What is the corresponding sand density $\rho_{\text {sand }}$ ? Solid silicon dioxide (the primary component of sand) has a density of $\rho_{\mathrm{SiO}_2}=2.600 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$.

category

physics

options

  1. 1.4 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  2. 1.2 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  3. 3.0 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  4. 1.6 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  5. 2.4 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  6. 1.8 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  7. 2.8 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  8. 2.2 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  9. 1.0 $10^3 \mathrm{~kg} / \mathrm{m}^3$
  10. 2.6 $10^3 \mathrm{~kg} / \mathrm{m}^3$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
10273
task_id
7af64b90-3a77-5681-adc0-b16fa5163f33
task_key
default--test--10273
task_revision_id
1
config / split
default / test

Official source

initial import