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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A satellite is revolving in a circular orbit at a height h from the earth's surface, such that h ≪ R where R is the radius of the earth. Assuming that the effect of the earth's atmosphere can be neglected. What should be the minimum change required in the speed so that the satellite could escape from the gravitational field of earth?

Options

  1. A2 - 1 g R
  2. B9 g R 2
  3. C2 g R
  4. Dg R

Correct answer

A. 2 - 1 g R

Step-by-step solution

Orbital velocity v 0 = G M ( R + h ) Velocity required to escape the gravitational field, v s = 2 G M ( R + h ) Change in velocity = 2 GM ( R + h ) - GM ( R + h ) If h < < R , Δ v = 2 G M R - G M R Δ v = 2 g R - g R

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