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Motion In Straight Line

Question
CBSEENPH11017464

Find the acceleration due to gravity at the surface of the earth in terms of density of the earth.

Solution
Acceleration due to gravity, g at the surface of the Earth is given by,
                         straight g equals GM over straight R squared 
Let straight rho be the density of body. 
The mass of the earth is, 
                        straight M equals fraction numerator 4 straight pi over denominator 3 end fraction straight R cubed straight rho
Therefore acceleration due to gravity in terms of density of the earth is, 
straight g equals fraction numerator straight G begin display style fraction numerator 4 straight pi over denominator 3 end fraction end style straight R cubed straight rho over denominator straight R squared end fraction equals fraction numerator 4 straight pi over denominator 3 end fraction ρRG