The acceleration due to gravity becomes g / 2 ( g= acceleration due to gravity on the surface of the earth) at a height equals to

Step-by-step solution

The acceleration due to gravity, g= G M R^2 (i) At a height h above the surface of the earth, the acceleration due to gravity is g^ = G M (R+h)^2 (ii) From Eqs. (i) and (ii), we get g g^ = ( R+h R )^2= (1+ h R )^2 g^ g^ = (1+ h R )⁻²= (1- 2 h R )^2 Here, g^ = g 2 g / 2 g = (1- 2 h R ) 2 h R = 1 2 or h= R 4