All Problems Universal Gravitation
Problem 1.212
Demonstrate that the gravitational force acting on a particle \(A\) inside a uniform spherical layer of matter is equal to zero.
1.212. First let us consider a thin spherical layer of substance (Fig. 9). Construct a cone with a small angle of taper and the vertex at the point \(A .\) The ratio of the areas cut out by the cone in the layer is \(d S_{1}: d S_{2}=r_{1}^{2}: r_{2}^{2}\). The masses of the cut volumes are proportional to their areas. Therefore these volumes will attract the particle \(A\) with forces equal in magnitude and opposite in direction. What follows is obvious.