Question

At what distance from the center of earth, the value of acceleration due to gravity g will be half that of the surfaces (R = Radius of earth) 

(A) 2R 

(B) R 

(C) 1.414 R 

(D) 0.414 R

Answer 1

Correct option: (C) 1.414 R

Explanation:

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