Q.

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

Moderate

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By Expert Faculty of Sri Chaitanya

a

ρ=3G4πrg

b

ρ=rG12πg

c

ρ=3g4πrG

d

ρ=3r4πgG

answer is 3.

(Detailed Solution Below)

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Detailed Solution

g=GMr2M=43πr3ρ⇒ g=G43πr3ρr2⇒ ρ=3g4πGr
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