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MHT CET20249 May 2024Evening ShiftPhysicsGravitationActual

A satellite is revolving around a planet in a circular orbit close to its surface. Let ' ' be the mean density and ' R ' be the radius of the planet. Then the period of the satellite is ( G = universal constant of gravitation)

Options

  1. A4 G
  2. BG
  3. C3 G
  4. D2 G

Correct answer

C. 3 G

Step-by-step solution

From Kepler's third law, aligned & T ^2= 4 ^2 r ^3 GM & ~T =2 r ^3 GM aligned As the satellite is very close to the planet, r=R . T =2 R ^3 GM ...(i) aligned & We know, Mass = Volume Density ( ) & = 4 3 R ^3 ...(ii) aligned Putting (ii) into (i) T=2 R^3 G 4 3 R^3 = 3 G

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