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 2r < x < 2R .

Step-by-step solution

Let the point of contact of the solid sphere and the hollow shell be the origin. The centers of both the solid sphere and the hollow shell lie on the same line passing through this point of contact. The center of the solid sphere is at a distance r from the point of contact, and the center of the hollow shell is at a distance R from the point of contact. The particle of mass m' is located at a distance x from the point of contact along this line. It is given that 2r Since x Since x > 2r , the particle lies strictly