Question

P=3g/4RG
Check through dimensional analysis

Answer 1

Answer:

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

(a)4piG/3gR (b)3piR/4gG

(c)3g/4piRG (d)piRg/12G

g equals fraction numerator G M over denominator R squared end fraction

space d e n s i t y space equals space fraction numerator m a s s over denominator v o l u m e end fraction

M a s s space equals space space d e n s i t y space x space v o l u m e

M equals space rho space x fraction numerator 4 πR cubed over denominator 3 R squared end fraction equals space space rho space x fraction numerator 4 πR over denominator 3 end fraction

P u t space v a l u e space o f space M space i n space g equals fraction numerator G M over denominator R squared end fraction

rho space equals space fraction numerator 3 g over denominator 4 πRG end fraction