What is the value of acceleration due to gravity on the surface of earth if the entire earth was made of gold ? (Radius of earth = 6400 km , Density of gold = 19.3 xx 10^(3) kg//m^3 and G = 6.67 xx 10^(-11) MKS)

What is the value of acceleration due to gravity on the surface of ear

1.	What is the value of acceleration due to gravity on the surface of earth if the entire earth was made of gold ? (Radius of earth = 6400 km , Density of gold = 19.3 xx 10^(3) kg//m^3 and G = 6.67 xx 10^(-11) MKS)
Answer» Solution :`IMPLIES` Here, `R_e = 6,400 km . = 64 xx 10^(5) m` `rho = 19.3 xx 10^(3) kg./m^3` `G = 6.67 xx 10^(-11) Nm^(2)//kg^(2)` Mass of EARTH Me = `4/3piRe_^3 rho` `implies g = (GM_e)/(R_e)` `implies g = (G)/(R_e^2) (4/3piRe^2rho)=4/3 piGrhoRe` `:. g = (4 xx 3.14 xx 6.67 xx 10^(-11) xx 19.3 xx 10^(3) xx 64 xx 10^5)/3` `:. g = (12.56 xx 6.6xx 19.3 xx 64 xx 10^(-3))/3` ` :. g = 34.49 m//s^2`