Among the statements provided, the one that is correct is:
One rotation of the sun takes less time than one of Earth’s rotations.
Here's a bit of detail to clarify:
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The sun’s rotation takes about 27 days: This is generally accurate for the solar equator, but the rotation period can vary depending on the latitude. The sun rotates differentially, meaning that different parts of it rotate at different rates.
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All parts of the sun rotate at the same rate: This is incorrect. The sun experiences differential rotation, meaning that the equator rotates faster than the poles.
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The gases at the sun’s poles rotate more quickly than the gases at the equator: This is also incorrect, as the opposite is true; gases at the equator rotate more quickly.
So, the correct statement is that one rotation of the sun takes less time than one of Earth's rotations (which is approximately 24 hours).