Answer:
0.31%
Explanation:
The acceleration due to gravity at sea level is:
g = GM / R²
where G is the gravitational constant, M is the mass of Earth, and R is the radius of the Earth.
The acceleration due to gravity a height h above sea level is:
g' = GM / (R+h)²
The percent variation is:
(g − g') / g
= 1 − g'/g
= 1 − [GM / (R+h)²] / [GM / R²]
= 1 − R² / (R+h)²
= 1 − (R / (R+h))²
The average radius of the Earth is 6370 km. The height of the balloon is 10 km.
1 − (6370 / (6370 + 10))²
0.0031
0.31%
