A body has a weight of 100 ~N on the surface of the Earth. At a certain altitude h above the surface, its weight is measured to be 36 ~N . If R is the radius of the Earth, the altitude h is

Step-by-step solution

The weight of a body at an altitude h is given by the exact formula: W' = W (1 + h R )^2 Given W = 100 ~N and W' = 36 ~N : 36 = 100 (1 + h R )^2 (1 + h R )^2 = 100 36 = 25 9 Taking the square root of both sides: 1 + h R = 5 3 h R = 5 3 - 1 = 2 3 h = 2R 3 Answer: 2R 3