Two planets A and B of equal mass are having their period of revolutions T A and T B such that T A = 2 T B .…

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA=2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
  1. 2rA2=rB3
  2. rA3=2rB3
  3. rA3=4rB3
  4. TA2-TB2=π2GMrB3-4rA3

Solution

From Kepler's law of periods,

T2∝R3

Therefore,

⇒TATB2=rArB3

⇒22=rA3rB3, ⇒rA3=4rB3

Asked in: JEE Main 2022 (28 Jun Shift 1)

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