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COMEDK2020PhysicsGravitation

A satellite can be in a geostationary orbit around a planet if it is at a distance R from the centre of the planet. If the planet starts rotating about its axis with double the angular velocity, then to make the satellite geostationary, its orbital radius should be

Options

  1. A2 R
  2. BR 2
  3. CR 2^ 1 / 3
  4. DR 4^ 1 / 3

Correct answer

D. R 4^ 1 / 3

Step-by-step solution

We know that, angular velocity, aligned &= 2 T T &= 2 T₂ T₁ &= ₁ ₂ &= ₁ 2 ₁ [ ₂=2 ₁ ] aligned array ll & T₂ T₁ = 1 2 & T₂= T₁ 2 array According to Kepler's law, aligned & T² R³ R₂ R₁ &= ( T₂ T₁ )^ 2 / 3 &= ( T₁ / 2 T )^ 2 / 3 &= ( 1 2 )^ 2 / 3 R₂ &= R₁ 2^ 2 / 3 &= R 4^ 1 / 3 aligned

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