Halliday, Resnick & Walker — Gravitation: Problem 46

46 A solid sphere has a uniformly distributed mass of $1.0 \times 10^4 \text{ kg}$ and a radius of $1.0 \text{ m}$. What is the magnitude of the gravitational force due to the sphere on a particle of mass $m = 2.0 \text{ kg}$ when the particle is located at a distance of (a) $1.5 \text{ m}$ and (b) $0.50 \text{ m}$ from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance $r \le 1.0 \text{ m}$ from the center of the sphere.