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JEE Main202120 Jul 2021Evening ShiftPhysicsGravitationActual

Consider a binary star system of star A and star B with masses m A and m B revolving in a circular orbit of radii r A and r B , respectively. If T A and T B are the time period of star A and star B , respectively, then:

Options

  1. AT A T B = r A r B 3 2
  2. BT A = T B
  3. CT A > T B (if m A > m B )
  4. DT A > T B (if r A > r B )

Correct answer

B. T A = T B

Step-by-step solution

1) From the centre of mass, we get M 1 R 1 = M 2 R 2 - - - - - - 1 2) Force acting on both starts i.e. gravitational force and centripetal force are balanced. GM 1 M 2 R 2 = M 1 V 1 2 R 1 = M 1 V 1 2 R 1 - - - - - - 2 As we know, V 1 = 2 πR 1 T 1 & V 2 = 2 πR 2 T 2 Substituting equation 3 in equation 2, we get M 1 R 1 T 1 2 = M 1 R 2 T 2 2 - - - - - - 4 From equation 1, we conclude in eqution 4 T 1 2 = T 2 2     or     T 1 = T 2

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