Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus. [mass of earth `5.97xx10^(24)`kg].

Explanation

The density of the nucleus of an atom
`rho_(N) = 2.3 xx 10^(17) kg m^(-3)`
`rho_(N) = rho_(E) = 2.3 xx 10^(17) kg m^(-3)`
Mass of the earth `M_(E) = 5.97 xx 10^(24)`kg
Density of the earth,
`rho_(E) = (m_(E))/(V)`
` = (m_(E))/(4/3 pi r^(3))`
`r^(3) = (m_(E))/((4)/(3) pi rho_(E) ) = (5.97 xx 10^(24))/(1.33 xx 3.14 xx2.3 xx 10^(17))`
` = (5.97 xx 10^(24))/(9.60526 xx 10^(17))`
`r^(3) = 0.6215 xx 10^(7) m^(3)`
` r = 183.85 m`
`r approx 180 m`.