Question

How do you use this equation to find 9.8 m/s?

Answer 1

Gravitational force due to the earth is given as

`F=(GM_em)/((r_e)^2)`

Here, G is the gravitational constant whose value is

`G=6.67*10^(-11)\text{ N m}^2\text{ /kg}^2`

The mass of the earth is

`M_e\text{ = 5.97}*10^(24)\text{ kg}`

The radius of the earth is

`r_e=6371*10^3\text{ m}`

Let m be the mass of any object.

Suppose the object is falling on the surface of the earth, so it will experience a force of mg.

Here, g is the acceleration due to gravity.

On equating both the forces,

`\begin{gathered} mg=\frac{GM_em\text{ }}{(r_e)^2} \\ g=(GM_e)/((r_e)^2) \end{gathered}`

On substituting the values, the value of g will be

`\begin{gathered} g=(6.67*10^(-11)*5.97*10^(24))/((6371*10^3)^2) \\ =9.81\text{ m/s}^2 \end{gathered}`