A circular ring of mass M and radius R and a spherical shell of mass 3M and radius R are arranged such that their centers are separated by a distance 3R and the plane of the circular ring is perpendicular to the line joining the centers. Gravitational field intensity at a point at a distance ‘R’ from the center of the ring is

Let P be the point of interest. Gravitational field at ‘P’ due to circular ring.  E1=GMx(x2+R2)32  here x=distance of the point from center of the ring; R=radius of the ring ⇒E1=GMRR2+R23/2=GMR22R3=GM22R2Gravitational field at ‘P’ due to spherical shell  E2=3GM2R2=3GM4R2  ∴Net gravitational field at a point ‘P’ is Enet=E2−E1   ∵E2>E1  towards center of spherical shell.Enet=3GM4R2−GM22R2 Enet=GMR234−122 towards center of spherical shell.