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JEE Main2013PhysicsGravitationActual

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?

Options

  1. AGmM 2 R
  2. BGmM 3 R
  3. C5 GmM 6 R
  4. D2 GmM 3 R

Correct answer

C. 5 GmM 6 R

Step-by-step solution

As we know, Gravitational potential cnergy = - GMm r and orbital velocity, v 0 = GM / R + h E f = 1 2 mv 0 2 - GMm 3 R = 1 2   m GM 3 R - GMm 3 R = GMm 3 R 1 2 - 1 = - GMm 6 R E i = - GMm R + K E i = E f Therefore minimum required energy, K = 5 GMm 6 R

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