The height at which the acceleration due to gravity becomes g 9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R , the radius of the earth is

Step-by-step solution

g^ = G M (R+h)^2 , acceleration due to gravity at height h aligned & g 9 = G M R^2 R^2 (R+h)^2 =g ( R R+h )^2 & 1 9 = ( R R+h )^2 R R+h = 1 3 & 3 R=R+h 2 R=h aligned