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JEE Main20245 Apr 2024Evening ShiftPhysicsGravitationActual

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : ( . Given = Radius of geo-stationary orbit for earth is 4.2 10^4 ~km )

Options

  1. A1.4 10^4 ~km
  2. B1.05 10^4 ~km
  3. C8.4 10^4 ~km
  4. D1.68 10^5 ~km

Correct answer

B. 1.05 10^4 ~km

Step-by-step solution

aligned & T = 2 r ^ 3 / 2 GM & T ₁ ~T ₂ = ( r ₁ r ₂ )^ 3 / 2 ( M ₂ M ₁ )^ 1 / 2 & 6 24 = ( r ₁ )^ 3 / 2 (4.2 10^4 )^ 3 / 2 ( M M / 4 )^ 1 / 2 & r ₁=1.05 10^4 ~km aligned

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