At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth as R )

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the Earth is given by g p = g R 2 ( R + h ) 2 . . . 1 The acceleration due to gravity at a depth h below the surface of the Earth is given by g q = g 1 - h R . . . 2 According to the given problem, g p = g q . . . 3 Equations (1), (2) and (3) imply that g 1 + h R 2 = g 1 - h R ⇒ 1 - h 2 R 2 1 + h R = 1 . . . 4 Take h R = x So, from equation (4), it follows that x 3 - x + x 2 = 0 ⇒ x 2 + x - 1 = 0 ⇒ x = 5 - 1 2 ⇒ h = R 2 ( 5 - 1 )