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What is the value of acceleration due to...

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)

Text Solution

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`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`
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