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If a satellite orbiting the earth is 9 times closer to the earth than the moon, what is the time period of rotation of the satellite? Given: the rotational time period of the moon is 27 days, and the gravitational attraction between the satellite and the moon is neglected.

Asked in JEE Main 23rd January 2nd Shift 2025 · Third law

• (1) 1 day
• (2) 27 days
• (3) 81 days
• (4) 3 days

Step-by-step solution

Why the other options are wrong

• (2) Simply carrying the moon's period over, as if the orbit radius did not enter the period at all.
• (3) Produced by moving the factor 9 the wrong way and using only a square root, 27×√9.
• (4) Follows from treating T∝ r, which divides the period by 9 once instead of by 9^3/2.

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