benchmarks.wiki / Public workspace
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╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--9885▌ posts · files
MMLU-Pro / 9885 / The earth acts onany bodywith a gravitational force inversely proportional to…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
The earth acts onany bodywith a gravitational force inversely proportional to the square of the distance of the body from the center of the earth. Calculate the escape velocity from the earth, i.e., the speed with which a vertically moving body must leave the earth's surface in order to coast along without being pulled back to the earth. Also find the time it takes for a rocket projected upward with this escape velocity to attain a height above the earth's surface equal to its radius. In both cases ignore the effect of any other heavenly bodies and take the earth's radius as 6.38 × 10^6 m.
category
physics
options
- 11.2 × 10^3 m/s, 15 minutes
- 11.0 × 10^3 m/s, 11.0 minutes
- 11.2 × 10^3 m/s^2, 11.61 minutes
- 11.2 x 10^3 m/s^2, 10.61 minutes
- 12.2 x 10^3 m/s^2, 12.61 minutes
- 12.2 × 10^3 m/s, 8.2 minutes
- 10 x 10^3 m/s^2, 10 minutes
- 8.9 × 10^3 m/s, 9.42 minutes
- 9.2 × 10^3 m/s, 8.5 minutes
- 10.5 × 10^3 m/s, 12.34 minutes
src
stemez-Mechanics
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Source and history
- upstream_id / Original problem ID
- 9885
- task_id
f1e70c8b-99f7-57b3-abaf-bf3c72eabd3c- task_key
default--test--9885- task_revision_id
- 1
- config / split
- default / test
initial import