As depicted in the figure, a solid sphere of mass m and radius r is positioned inside a hollow thin spherical shell of mass M and radius R . A particle of mass m' is located on the line connecting the two centres at a distance x from the point of contact of the sphere and the shell. Determine the magnitude of the resultant gravitational force on this particle due to the sphere and the shell, given that r

Step-by-step solution

The particle is located at a distance x from the point of contact, where r The gravitational field inside a uniform hollow spherical shell is zero. Therefore, the force exerted by the shell of mass M on the particle is zero. The center of the solid sphere is at a distance r from the point of contact. The distance of the particle from the center of the solid sphere is d = x - r . Since r The gravitational force on a particle of mass m' at a distance d from the center of a uniform solid sphere of mass m and radius r