Question

At what height above the earth's surface, the value of gis same as that at a depth of 100 km?

Answer 1

acceleration due to gravity at height h is given as

g' = g (1 - 2h/R)

acceleration due to gravity at a depth r is given as

g'' = g(1 - r/R)

now we are given that g' = g''

so,

g (1 - 2h/R) = g(1 - r/R)

or

(1 - 2h/R) = (1 - r/R)

=> 2h/R = r/R

or

h = r/2 = 100/2 = 50 km