At what height above the surface of the earth will the weight of a body become 64 % of its weight on the surface of the earth? (where R is the radius of the earth)

Step-by-step solution

Let the weight of the body on the surface of the earth be W = mg . The weight at a height h is given by W_h = W (1 + h R )^2 . Given that W_h = 64 % of W = 0.64 W . Equating the two expressions: 0.64 W = W (1 + h R )^2 (1 + h R )^2 = 1 0.64 = 100 64 = 25 16 Taking the square root on both sides: 1 + h R = 5 4 h R = 5 4 - 1 = 1 4 h = R 4 Using the approximate formula W_h = W (1 - 2h R ) leads to the incorrect answer 9R 50 , as the approximation is only valid for h R . Answer: R 4