Walker, Halliday & Resnick — Gravitation: Problem 64

64 Mountain pull. A large mountain can slightly affect the direction of “down” as determined by a plumb line. Assume that we can model a mountain as a sphere of radius \( R = 1.80 \text{ km} \) and density (mass per unit volume) \( 2.6 \times 10^3 \text{ kg/m}^3 \). Assume also that we hang a \( 0.50 \text{ m} \) plumb line at a distance of \( 3R \) from the sphere’s center and such that the sphere pulls horizontally on the lower end. How far would the lower end move toward the sphere?