Question

The acceleration due to gravity near the earth's surface is $9.8{\text{m/s}}^2$, and the earth's radius is $6400\text{km}$. From this data, calculate the mass of the earth.
$[G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{/kg}}^2]$

• A. $6\times {10}^{27}\text{kg}$
• B. $3\times {10}^{24}\text{kg}$
• C. $3\times {10}^{27}\text{kg}$
• D. $6\times {10}^{24}\text{kg}$

Answer 1

The correct option is D $6\times {10}^{24}\text{kg}$

We know that,
$g=\frac{GM}{R^2}$

$\Rightarrow M=\frac{g{R}^2}{G}$

$\Rightarrow M=\frac{9.8\times (6400\times {10}^3{)}^2}{6.67\times {10}^{-11}}=6\times {10}^{24}\text{kg}$