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Question: Answered & Verified by Expert
The ratio of the energy required to raise a satellite upto a height \( h \) above the earth of radius \( R \) to that the kinetic energy of the satellite into that orbit is
PhysicsGravitationJEE Main
Options:
  • A \( \mathrm{R}: \mathrm{h} \)
  • B \( h: R \)
  • C \( \mathrm{R}: 2 \mathrm{~h} \)
  • D \( 2 \mathrm{~h}: \mathrm{R} \)
Solution:
2800 Upvotes Verified Answer
The correct answer is: \( 2 \mathrm{~h}: \mathrm{R} \)
Energy required to raise the satellite to a height h from surface of earth is given by,
U = - GmM R + h - - GmM R = GMmh R R + h
Kinetic energy of satellite is given by,
K = 1 2 mv 0 2 = 1 2 m GM R + h
∴     U K = 2 h R

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