Given parameters:
Height of Everest = 8848m
Acceleration due to gravity on earth = 9.8m/s²
Radius of the earth = 6400km = 6400000m
Unknown:
Acceleration due to gravity at the peak of Everest =?
Solution:
According to Newton's law of universal gravitation, we have that acceleration due to gravity is proportional to the altitude.
To solve this problem, use the mathematical expression below;
g[tex]_{e}[/tex] = g(1 - [tex]\frac{2h}{R}[/tex])
where g[tex]_{e}[/tex] is gravity on top of Everest
g is the gravity on the earth surface
h is the height of the mountain
R is the radius of the earth
g[tex]_{e}[/tex] = 9.8 (1 -[tex]\frac{2 x 8848}{6400000}[/tex] )
g[tex]_{e}[/tex] = 9.8 (1-0.002765) = 9.77m/s²
The acceleration due to on top of Everest is 9.77m/s²
