At what height above the surface of the earth will the acceleration due to gravity be `25%` of its value on the surface of the earth ? Assume that the radius of the earth is 6400 km .

Explanation

Given : `g_(h) = 25%` of `g = (25)/(100) xx g = (1)/(4) g`.
`g_(h) = g(R/(R + h))^(2)`
`1/4 g = g (R/(R+h))^(2)`
`:. R/(R + h) = 1/2`
[Taking square root on both sides]
`2R = R + h`
`:. 2R - R = h`
`:. h = R`
`= 6400 km`.