A body is taken to a height h = R 2 above the Earth's surface, where its weight is W₁ . The same body is then taken to a depth d = R 2 below the Earth's surface, where its weight is W₂ . If R is the radius of the Earth, the ratio W₁ : W₂ is

Step-by-step solution

The weight of a body at an altitude h is given by: W_ h = W (1 + h R )^2 For h = R 2 : W₁ = W (1 + 1 2 )^2 = W ( 3 2 )^2 = 4W 9 The weight of a body at a depth d is given by: W_ d = W (1 - d R ) For d = R 2 : W₂ = W (1 - 1 2 ) = W 2 The ratio of the weights is: W₁ W₂ = 4W 9 W 2 = 8 9 Thus, the ratio W₁ : W₂ is 8 : 9 . Answer: 8 : 9