Question

How to calculate the value of $g$ at the surface of Earth? (Mass $=5.97x{10}^{24}kg$, Radius= $6378km$)

Answer 1

Step 1: List the known values

Mass of earth $M=5.97x{10}^{24}kg$

Radius of earth $R=6378km$

We know that the value of gravitation constant, $G=6.67\times {10}^{-11}Nm²/kg²$

Step 2: Calculate the acceleration due to gravity

We know that the acceleration due to gravity can be given as,

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

Upon substituting the values we get,

$g=\frac{6.67\times {10}^{-11}\times 5.97\times {10}^{24}\times {10}^3}{{\left(6378\times {10}^3\right)}^2}$

$=9.837m/s^2$

Here we have converted the mass from $kg$ to $g$ since the acceleration is calculated in $m/s^2$.

Hence, the value of $g$ on earth is $9.837m/s^2$.