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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A small planet is revolving around a very massive star in a circular orbit of radius r with a period of revolution T . If the gravitational force between the planet and the star is proportional to r 5 / 2 , then T will be proportional to

Options

  1. Ar 3 / 2
  2. Br 5 / 3
  3. Cr 7 / 4
  4. Dr 3

Correct answer

C. r 7 / 4

Step-by-step solution

According to the question, the gravitational force between the planet and the star is ( F 1 R ^ 5 / 2 ) ( F = GMm R ^ 5 / 2 ) Where M and M be masses of star and planet respectively. For motion of planet in circular orbit, ( mR ²= GMm R ^ 5 / 2 ) ( mR ( 2 T )²= GMm R ^ 5 / 2 ) ( ( = 2 T ) ) ( 4 ² ~T ² = GM R ^ 7 / 2 T ²= 4 ² GM R ^ 7 / 2 ) ( T ² R ^ 7 / 2 ) or ( T ² R ^ 7 / 4 )

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