Question

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

Answer 1

Given,

$g=9.8m/s^2,G=6.673\times {10}^{-11}N{m}^2/kg,R=6400km$

So,

$g=\frac{Gm}{R^2}$

$=\frac{G}{R^2}\times \frac{4}{3}\pi R^3\times \rho$ Since $m=\frac{4}{3}\pi R^3\times \rho$

$\frac{4}{3}\times \frac{22}{7}\times 6.66\times {10}^{-11}\times 6.4\times {10}^6\times 5.5\times {10}^3$

$=9.82m/s^2$