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JEE Main201911 Jan 2019Morning ShiftPhysicsGravitationActual

A satellite is revolving in a circular orbit at a height h from the carth surface, such that h < < R where R is the radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

Options

  1. A2 g R
  2. Bg R
  3. Cg R 2
  4. Dg R ( 2 -1)

Correct answer

D. g R ( 2 -1)

Step-by-step solution

For a satellite orbiting close to the earth, orbital velocity is given by v₀= g(R+h) = g R Escape velocity ( v _ e ) is v_ e = 2 g(R+h) = 2 g R [ h < c R v=v_ e -v₀=( 2 -1) g R

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