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JEE MainPhysicsGravitation

A satellite is revolving around a planet in a circular orbit of radius R with an orbital speed v . If it is moved to a new circular orbit where its orbital speed becomes v 2 , the radius of the new orbit is :

Options

  1. A2R
  2. B4R
  3. CR 2
  4. DR 4

Correct answer

B. 4R

Step-by-step solution

The orbital speed of a satellite in a circular orbit of radius r is given by v = GM r . For the initial orbit: v = GM R For the new orbit, the speed is v' = v 2 . Let the new radius be R' . v 2 = GM R' Substituting the value of v from the first equation: 1 2 GM R = GM R' Squaring both sides: 1 4 ( GM R ) = GM R' R' = 4R Answer: 4R

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