The weight of an object decreases by 75 % when it is taken to a height h above the surface of the earth. It is observed that the weight of the same object also decreases by 75 % when it is taken to a depth d below the surface of the earth. If R is the radius of the earth, the ratio h d is

Step-by-step solution

Let the acceleration due to gravity on the surface of the earth be g . A decrease of 75 % in weight means the weight becomes 25 % of its original value. Thus, the acceleration due to gravity at both the height h and the depth d is g' = g 4 . For height h , the exact formula is: g' = g (1 + h R )^2 g 4 = g (1 + h R )^2 (1 + h R )^2 = 4 1 + h R = 2 h = R For depth d , the formula is: g' = g (1 - d R ) g 4 = g (1 - d R ) 1 - d R = 1 4 d R = 3 4 d = 3R 4 The ratio of height to depth is: h d = R 3R 4 = 4 3 Answer: 4 3