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JEE Main202228 Jun 2022Morning ShiftPhysicsGravitationActual

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 . These planets are revolving in the circular orbits of radii r A and r B respectively. Which out of the following would be the correct relationship of their orbits?

Options

  1. A2 r A 2 = r B 3
  2. Br A 3 = 2 r B 3
  3. Cr A 3 = 4 r B 3
  4. DT A 2 - T B 2 = π 2 G M r B 3 - 4 r A 3

Correct answer

C. r A 3 = 4 r B 3

Step-by-step solution

From Kepler's law of periods, T 2 ∝ R 3 Therefore, ⇒ T A T B 2 = r A r B 3 ⇒ 2 2 = r A 3 r B 3 , ⇒ r A 3 = 4 r B 3

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