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MMLU-Pro / 9957 / Under some circumstances, a star can collapse into an extremely dense object…

Problem

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

question

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 101410^14 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was $7 \tims 10^5$ km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed (in rad/s) of the neutron star.
Plain-text mathematical notation (without MathML)
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 10¹4 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was $7 \tims 10^5$ km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed (in rad/s) of the neutron star.
Original LaTeX notation
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly $10^14$ times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was $7 \tims 10^5$ km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed (in rad/s) of the neutron star.

category

physics

options

  1. 600.0
  2. 3000.0
  3. 4600.0
  4. 18400.0
  5. 1500.0
  6. 9200.0
  7. 2300.0
  8. 1150.0
  9. 575.0
  10. 11.5

src

theoremQA-Physics

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Source and history

upstream_id / Original problem ID
9957
task_id
94418170-ed88-59b3-8d6c-047e9effd7d8
task_key
default--test--9957
task_revision_id
1
config / split
default / test

Official source

initial import