At what depth below surface of the earth, the acceleration due to gravity will be half its value of that at 1600 km above the surface of the earth?

Step-by-step solution

Acceleration due to gravity at a height, g h = g 1 - 2 h R ⇒ g h = g 1 - 2 × 1600 × 10 3 6400 × 10 3 ⇒ g h = g 1 - 0 . 5 ⇒ g h = 5   m   s - 2 Given, 2 . 5 = 10 1 - d R ⇒ 1 4 = 1 - h R ⇒ 3 4 = d R ⇒ d = 3 4 × 6400 × 10 3 ⇒ h = 4 . 8 × 10 6   m