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A planet has a mass M₁ and radius R₁ . The value of acceleration due to gravity on its surface is g₁ . There is another planet 2 , whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2 ?

Options

  1. Ag ₁
  2. B2 ~g ₁
  3. Cg ₁ / 2
  4. Dg ₁ / 4

Correct answer

C. g ₁ / 2

Step-by-step solution

The acceleration experienced by the mass M ₁ , on planet 1 is given by g ₁= GM ₁ / R ₁^2 , similarly the g ₂= G ₂ M ₁ / 4 R ₁ ^2 , hence, g ₁ / g ₂=2 / 1 or g ₂= g ₁ / 2

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