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JEE Main20241 Feb 2024Evening ShiftPhysicsGravitationActual

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T . If the force of attraction between planet and star is proportional to R - 3 / 2 then choose the correct option :

Options

  1. AT 2 ∝ R 5 / 2
  2. BT 2 ∝ R 7 / 2
  3. CT 2 ∝ R 3 / 2
  4. DT 2 ∝ R 3

Correct answer

A. T 2 ∝ R 5 / 2

Step-by-step solution

Let the gravitational force of attraction be F = G M m R 3 / 2 . Now, this gravitational force will provide the required centripetal force. Therefore, G M m R 3 / 2 = m ω 2 R ⇒ ω 2 ∝ 1 R 5 / 2 ∵ T = 2 π ω ⇒ T 2 ∝ R 5 / 2

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