Knowing the values of the mass and radius of the Earth, the acceleration due to the gravity (g) of Earth is 9.80 m/s².
We can calculate the acceleration due to gravity of the Earth with Newton's law of universal gravitation:
[tex] F = \frac{GmM}{r^{2}} [/tex] (1)
Where:
F: is the gravitational force
G: is the gravitational constant = 6.67x10⁻¹¹ Nm²kg⁻²
M: is the Earth's mass = 5.96x10²⁴ kg
r: is the Earth's radius = 6371 km
m: is the mass of an object
The gravitational force is also equal to:
[tex] F = ma [/tex] (2)
Where:
a = g = acceleration due to gravity
Hence, by entering equation (2) into (1) we have:
[tex] \frac{GmM}{r^{2}} = mg [/tex]
[tex] g = \frac{GM}{r^{2}} = \frac{6.67 \cdot 10^{-11} Nm^{2}/kg^{2}*5.96\cdot 10^{24} kg}{(6.371 \cdot 10^{6} m)^{2}} = 9.80 m/s^{2} [/tex]
Therefore, the value of g is 9.80 m/s².
You can learn more about Newton's law of universal gravitation here: https://brainly.com/question/9373839?referrer=searchResults
I hope it helps you!
