Question

Obtain the mass of earth from the following data:

$$\begin{gathered} g=9.8m{s}^{-2} \\ R=6.38\times {10}^{6}m \\ G=6.67\times {10}^{-11}M.K.S.units. \end{gathered}$$

Answer 1

Step 1: Given data

$$\begin{gathered} g=9.8m{s}^{-2} \\ R=6.38\times {10}^{6}m \\ G=6.67\times {10}^{-11}M.K.S.units. \end{gathered}$$

Step 2: Formula for acceleration due to gravity

$$\begin{gathered} g=G\times \frac{M}{R^2} \\ \Rightarrow M=\frac{g\times R^2}{G} \end{gathered}$$

Step 3: Substituting the given values

$$\begin{gathered} M=\frac{g\times R^2}{G} \\ =\frac{9.8m{s}^{-2}\times {\left(6.38\times {10}^{6}m\right)}^2}{6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}} \\ =5.98\times {10}^{24}kg \end{gathered}$$

Hence, the mass of the earth is $5.98\times {10}^{24}kg$.