Question

At at what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R =radius of earth)

Answer 1

At height h,  g' = g[R / (R + h)]² 

(g/2) = g[R / (R + h)]² 

(1 / √2) = [R / (R + h)]

R + h = √2 R

h = R(√2 – 1)

h = 0.414 R

hence distance from centre = R + h

= R + 0.414 R 

= 1.414 R