The value of acceleration due to gravity at a height of 10 ~km from the surface of earth is x . At what depth inside the earth is the value of the acceleration due to gravity has the same value x ?

Step-by-step solution

The value of acceleration due to gravity at height (h=10 ~km ) is x . array ll i.e., & g_ h =x & g (1+ h R_ e )² =x & g (1- 2 h R_ e )=x ...(i) array The value of acceleration due to gravity at depth d below the surface of earth, array r g_ d =x g (1- d R_ e )=x ...(ii) array From Eqs. (i) and (ii), we have g (1- 2 h R_ e )=g (1- d R_ e ) 1- 2 h R_ e =1- d R_ e 2 h R_ e = d R_ e d=2 h=2 10=20 ~km