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MMLU-Pro / 9141 / Perform an explicit calculation of the time average (i.e., the average over one…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Perform an explicit calculation of the time average (i.e., the average over one complete period) of the potential energy for a particle moving in an elliptical orbit in a central inverse-square-law force field. Express the result in terms of the force constant of the field and the semimajor axis of the ellipse.

category

physics

options

  1. -1 $\frac{k}{a}$
  2. $\frac{k}{2a}$
  3. $-2 \frac{k}{2a}$
  4. -2 $\frac{k}{a}$
  5. 1 $\frac{k}{a}$
  6. $2 \frac{k}{a}$
  7. $-3 \frac{k}{a}$
  8. 0 $\frac{k}{a}$
  9. $\frac{1}{2} \frac{k}{a}$
  10. $- \frac{k}{2a}$

src

scibench-class

Discussion

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Source and history

upstream_id / Original problem ID
9141
task_id
e000a751-04a2-5c4d-918c-4044bb5210de
task_key
default--test--9141
task_revision_id
1
config / split
default / test

Official source

initial import