Mass and Density of Earth

The mass of earth is 6.018 × 10²⁴kg

Since, the acceleration due to gravity is given by

$\displaystyle g=\dfrac{{GM}}{{{{R}^{2}}}}$

$\displaystyle \therefore M=\dfrac{{g{{R}^{2}}}}{G}$

$ \displaystyle \because G=6.67\times {{10}^{{-11}}}\text{ N}{{\text{m}}^{\text{2}}}\text{k}{{\text{g}}^{{\text{-2}}}}$ and $\displaystyle g=9.8\text{ m}{{\text{s}}^{{\text{-2}}}}$ and $\displaystyle R=6.4\times {{10}^{5}}\text{ m}$

$\displaystyle \begin{array}{l}\therefore M=\dfrac{{9.8\times {{{\left( {6.4\times {{{10}}^{5}}} \right)}}^{2}}}}{{6.67\times {{{10}}^{{-11}}}}}\\\Rightarrow M=6.018\times {{10}^{{24}}}\text{ kg}\end{array}$