Question

The value of g on the surface of the earth is__________

Answer 1

Step 1: Given data

$MassofEarth,M=5.97\times {10}^{24}kg$

$RadiusofEarth,R=6375\times {10}^{3}m$

$GravitationalCons\tan t,G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Step 2: Formula used

$\begin{array}{l}g=\frac{GM}{R^2}\end{array}$

Here,

$g$ is the acceleration due to gravity.

$M$ is the mass of the planet.

$R$ is the radius of the planet.

$G$ is the Universal Gravitational constant.

Step 3: Calculating the value of g

Acceleration due to gravity is given by,

$\begin{array}{l}g=\frac{GM}{R^2}\end{array}$

$\begin{array}{l}\Rightarrow \frac{6.67\times {10}^{-11}N{m}^2/k{g}^2\times 5.97\times {10}^{24}kg}{(6375\times {10}^{3}m{)}^2}\end{array}$

$\begin{array}{l}\Rightarrow 9.78m/s^2\end{array}$

Therefore, the value of g on the surface of the earth is $9.78m/s^2$.