Question

Radius of earth is equal to $6\times {10}^{6}m$. Acceleration due to gravity is equal to $9.8m/s^2$. Gravitational constant $G$ is equal to $6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$. Then mass of the earth is:-

• A. $6.0\times {10}^{24}kg$
• B. $5.3\times {10}^{24}kg$
• C. $5.9\times {10}^{24}kg$
• D. $6.6\times {10}^{24}kg$

Answer 1

The correct option is A $6.0\times {10}^{24}kg$

We know that,

$G=\frac{GM}{R^2}$ where $g$= acceleration due to gravity, $G$= Gravitational constant

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

$\Rightarrow M=\frac{9.8\times 6.4\times {10}^{12}}{6.67\times {10}^{-11}}$

$\Rightarrow M=6.08\times {10}^{24}kg$