Question

If the radius of earth is R then height H at which value of g become one- fourth is

Answer 1

Answer:

g = $\frac{GM}{R^{2} }$

at some height H let the acceleration due to gravity be g'

g' = $\frac{GM}{(R+H)^{2} }$

but g' = g/4

solving for H,  

$\frac{g}{4} = g'\\ \\\frac{GM}{4R^2} = \frac{GM}{(R+H)^2} \\R+H = 2R \\\\H = R$

The g becomes one-fourth at a height H = R (radius of earth) from the earths surface