Halliday, Resnick & Walker — Gravitation: Problem Problem_23

One model for a certain planet has a core of radius \(R\) and mass \(M\) surrounded by an outer shell of inner radius \(R\), outer radius \(2R\), and mass \(4M\). If \(M = 4.1 \times 10^{24} \text{ kg}\) and \(R = 6.0 \times 10^6 \text{ m}\), what is the gravitational acceleration of a particle at points (a) \(R\) and (b) \(3R\) from the center of the planet?