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JEE Main202124 Feb 2021Morning ShiftPhysicsGravitationActual

Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The period of revolution is

Options

  1. A2 π d 3 3 G m
  2. B2 π 3 G m d 3
  3. C1 2 π 3 G m d 3
  4. D1 2 π d 3 3 G m

Correct answer

A. 2 π d 3 3 G m

Step-by-step solution

F = G 2 m m d 2 = 2 m ω 2 d / 3 G m d 2 = ω 2 d 3 ⇒ ω 2 = 3 G m d 3 ⇒ ω = 3 G m d 3 ⇒ T = 2 π ω = 2 π d 3 3 G m

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