The mass of moon is (1 /81 )th the of mass of earth and g on moon is(1 /6)th the of g on earth. The ratio of moon to earth radii is
a) 81
/6
b) 6
/81
c) √2/√ 27
d) √2/ √48
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Answer:
Option C
Explanation:
Consider earth to be object 1 and moon to be object 2.
g₁ = GM₁ / R₁²
g₂ =GM₂/ R₂²
g₁ = 6 x g₂
GM₁R₂² = 6 x GM₂R₁²
Cancel G on both sides and rearrange,
(R₂/R₁)² = 6x (M₂/M₁)
= 6/81 = 2/27
R₂/R₁ = √2/√27
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