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Question

The diameters of two planets are in ratio 4:1. Their mean densities have ratio 1:2. The ratio of g on the planets will be
  1. 1:2
  2. 1:4
  3. 2:1
  4. 4:1


Solution

The correct option is C 2:1
Given: ratio of diameter
D1D2=41
R1R2=41
and ratio of densities
ρ1ρ2=12
gg=GM1GM2(R2R1)2
=G43πR31G43πR32(R2R1)2(ρ1ρ2)
gg=(ρ1ρ2)(R1R2)
gg=12×41=21

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