If ρ is the mean density of the earth, r its radius, g the acceleration due to gravity and G the gravitational constant, on the basis of dimensional consistency, the correct expression is

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ρ=3G4πrg

ρ=rG12πg

ρ=3g4πrG

ρ=3r4πgG

answer is C.

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Detailed Solution

g=GMr2M=43πr3ρ⇒ g=G43πr3ρr2⇒ ρ=3g4πGr

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