Mass and Density of Earth
Category : JEE Main & Advanced
Newton's law of gravitation can be used to estimate the mass and density of the earth.
As we know \[g=\frac{GM}{{{R}^{2}}}\], so we have \[M=\frac{g{{R}^{2}}}{G}\]
\[\therefore \] \[M=\frac{9.8\times {{(6.4\times {{10}^{6}})}^{2}}}{6.67\times {{10}^{-11}}}=5.98\times {{10}^{24}}kg\approx {{10}^{25}}kg\]
and as we know \[g=\frac{4}{3}\pi \rho GR\], so we have \[\rho =\frac{3g}{4\pi GR}\]
\[\therefore \] \[\rho =\frac{3\times 9.8}{4\times 3.14\times 6.67\times {{10}^{-11}}\times 6.4\times {{10}^{6}}}=5478.4\ kg/{{m}^{3}}\]
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