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MHT CET202015 Oct 2020Morning ShiftPhysicsGravitationActual

The acceleration due to gravity on moon is ( 1 6 )^ th times the acceleration due to gravity on earth. If the ratio of the density of earth ' _ e ' to the density of moon _ m ' is 5 3 , then the radius of moon ' Rm ' in terms of the radius of earth 'Re' is

Options

  1. A( 7 6 ) Re
  2. B( 3 18 ) Re
  3. C( 5 18 ) Re
  4. D( 1 2 3 ) Re

Correct answer

C. ( 5 18 ) Re

Step-by-step solution

g _ m g _ e = 1 6 _ e _ m = 5 3 R _ m R _ e =? g _ m g _ e = M _ m R _ m ² R _ e ² M _ e = 4 3 R _ m ³ _ m R _ m ² R _ e ² 4 3 R _ e ³ _ e = R _ m _ m R _ e _ e = 1 6 R _ m R _ e = 1 6 _ e _ m = 1 6 5 3 = 5 18

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