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JEE MainPhysicsGravitation

A satellite is revolving in a circular orbit around a planet. To transfer the satellite to a higher circular orbit, external work equal to exactly half of its initial kinetic energy is supplied to it. The ratio of its new time period of revolution to its initial time period is:

Options

  1. A2
  2. B4
  3. C1 2 2
  4. D2 2

Correct answer

D. 2 2

Step-by-step solution

For a satellite in a circular orbit, the relation between total energy ( E ) and kinetic energy ( K ) is E = -K . Let the initial kinetic energy be K₁ . The initial total energy is E₁ = -K₁ . The work done to transfer the satellite is W = 0.5 K₁ . The final total energy E₂ is: E₂ = E₁ + W = -K₁ + 0.5 K₁ = -0.5 K₁ Since the total energy of a satellite in a circular orbit of radius r is inversely proportional to r ( E - 1 r ), we have: E₂ E₁ = r₁ r₂ -0.5 K₁ -K₁ = r₁ r₂ 1 2 = r₁ r₂ r₂ = 2r₁ According to Kepler's Third

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