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NTA Abhyas JEE Main2020PhysicsGravitationPractice

Suppose the gravitational force varies inversely as the n t h power of the distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to

Options

  1. AR - n
  2. BR n - 1 2
  3. CR n + 1 2
  4. DR n

Correct answer

C. R n + 1 2

Step-by-step solution

Gravitational force = G M m d 2 (Newton's law) But in this case, F = G M m R n and it provides the necessary centripetal force m v 2 R ∴ m v 2 R = G M m R n ∴ v = G M R n - 1 and the period T of a planet, T = 2 π R v ∴ T = 2 π R R n - 1 G M = 2 π R n + 1 G M = 2 π G M ⋅ R n + 1 2 ∴ T ∝ R n + 1 2

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