Question

If mass of Earth is $6\times {10}^{24}kg$, radius of Earth is $6.4\times {10}^{6}m$ and the gravitational constant is $6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$, calculate the value of $g$.

Answer 1

Step 1: Given data

Mass of the earth, $M=6\times {10}^{24}kg$

Radius of the earth, $R=6.4\times {10}^{6}m$

Gravitational constant, $G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Step 2: Finding the value of $g$

Acceleration due to gravity $g$can be given as below:

$g=\frac{GM}{R^2}$

Substitute the values in the above formula.

$g=\frac{6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}\times 6\times {10}^{24}kg}{{(6.4\times {10}^{6}m)}^2}$

$g=\frac{6.7\times 6\times {10}^{-11}\times {10}^{24}}{6.4\times 6.4\times {10}^{12}}$

$g=0.981\times {10}^{(-11+24-12)}$

$g=0.981\times 10$

$g=9.81m/s^2$

Hence, the value of $g$ is $9.81m/s^2$.