Question

Assuming the earth to be a homogeneous sphere, determine the density of the earth from following data. $[g=9.8m/s^2,G=6.673\times {10}^{-11}N{m}^2/k{g}^2,R=6400km]$

Answer 1

$R=6400\times {10}^{3}m=6.4\times {10}^{6}m$

$p=5.5\frac{g}{cc}=5.5\times {10}^3=\frac{kg}{m^3}$

$g=\frac{GM}{R^2}=\frac{G}{R^2}\times \frac{4}{3}\pi R^{3}p=\frac{4}{3}\pi GRp=\frac{4}{3}\times \frac{22}{7}\times 6.66\times {10}^{-11}\times 6.4\times {10}^6\times 5.5\times {10}^3=9.82m{s}^{-2}$