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Manipal MET2021PhysicsGravitation

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T . If the gravitational force of attraction between the planet and the star is proportional to R^ -5 / R , then T^2 is proportional to :

Options

  1. AR^3
  2. BR^ 7 / 2
  3. CR^ 3 / 2
  4. DR^ 3.75

Correct answer

B. R^ 7 / 2

Step-by-step solution

Gravitational force (= G M m R^ 5 / 2 ) provides the necessary centripetal force (i e, m R ^2 ) . So, G M m R^ 5 / 2 =m R ^2=m R ( 2 T )^2= 4 ^2 m R T^2 or T^2= 4 ^2 R^ 7 / 2 G M i.e, T^2 R^ 7 / 2

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