variation of 'g' with height

g_h = GM/(R+h)²

g at the earth surface, h = 0.

g_s = GM/R²

g_h = GM/(R+h)² = 0.25g_s

1/(R+h)² = 0.25/R²

4R² = R² + 2Rh + h²

2Rh + h² - 3R² = 0

h = [-2R±(4R²+12R²)^1/2]/2

So h = R

The value of g becomes 25% of its value on the surface of earth, at a height equal to the radius of the earth i.e. 6400 km.

Regards,

Team,

TopperLearning.