The weight of an object decreases by 64 % when it is taken to a height h above the surface of the earth. If R is the radius of the earth, the value of h is

Step-by-step solution

Let the acceleration due to gravity on the surface of the earth be g . Since the weight decreases by 64 % , the new weight is 100 % - 64 % = 36 % of the original weight. Therefore, the acceleration due to gravity at height h is g' = 0.36g = 9 25 g . The formula for acceleration due to gravity at a height h is given by: g' = g (1 + h R )^2 Substituting the value of g' : 9 25 g = g (1 + h R )^2 (1 + h R )^2 = 25 9 Taking the square root on both sides: 1 + h R = 5 3 h R = 5 3 - 1 = 2 3 h = 2R 3 Answer: 2R 3