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MHT CET20226 Aug 2022Morning ShiftPhysicsGravitationActual

Two spherical planets A and B have the same mass but their densities are in a ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of A to its value at the surface of B is

Options

  1. A8: 1
  2. B4: 1
  3. C1: 4
  4. D8:1

Correct answer

C. 1: 4

Step-by-step solution

Given: ₁: ₂=1: 8 and m₁=m₂ We know that, = m V aligned & ₁ V₁= ₂ V₂ & ₁ 4 3 R₁^3= ₂ 4 3 R₂^3 & ( R₁ R₂ )= ₂ ₁ = 8 1 & ( R₁ R₂ )= 2 1 aligned As we know that the acceleration due to gravity, g= G M R^2 aligned & g= G R^2 4 3 R^3= 4 3 G R & g₁ g₂ = ( ₁ ₂ ) ( R₁ R₂ ) & g₁ g₂ = 1 8 2= 1 4 New soln aligned

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