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MHT CET202313 May 2023Evening ShiftPhysicsGravitationActual

If two planets have their radii in the ratio x: y and densities in the ratio m: n , then the acceleration due to gravity on them are in the ratio

Options

  1. Any / mx
  2. Bmy / nx
  3. Cnx / my
  4. Dmx / ny

Correct answer

D. mx / ny

Step-by-step solution

We know, g = GM R ^2 If the density is d, then M= 4 3 R^3 d ( M=V d) g 4 3 GRd Given, R ₁ R ₂ = x y and d ₁ ~d ₂ = m n g ₁= 4 3 GR ₁ ~d ₁ g ₂= 4 3 GR ₂ ~d ₂ Therefore, g ₁ ~g ₂ = R _ l ^ R ₂^ d ₁^ d ₂ g ₁ ~g ₂ = xm yn

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