Calculate the average density of earth in terms of g, G and R.

Explanation

We know that, `(g=(GM)/(R^(2)))` where M = Mass of the earth, R = Radius of the earth.
`So," ""mass of the earth", M=(gR^(2))/(G)`
If the earth is considered as a shopere of radius R and of material of density `rho` then
`"Mass of earth = volume of the earth" xx "density"" "[because"volume of sphere"=(4)/(3)pir^(3)]`
`M=(4)/(3)piR^(3)rho`
From Eq. (i), we get
`:." "(4)/(3)piR^(3)rho=(gR^(2))/(G)`
`" "rho=(3g)/(4piGR)`