A spherical cavity is made in a lead sphere of radius R such than its surface touches the outside surface of the lead sphere and passes through its centre. The mass of the lead sphere before hollowing was M. The force of attraction that this sphere would exert on a particle of mass m, which lies at a distance d from the centre of the lead sphere on the straight line joining the centres of the sphere and the centre of the cavity as shown in the figure is

Force calculation of gravitational field intensity inside the cavity. Gravitational field intensity without cavity, E1=GMdR3−i^Radius of cavity R'=R2,r=R2−d  i.e., inside the cavity the gravitational field intensity,Intensity due to remaining part E2=GM'rR'3 E2=GM/8R2−di^R23 E2=GMR3R2−di^ Gravitational field intensity due to cavity portion of radius  R2−d  net intensity E=E1-E2 E=GMdR3−i^+GMR3R2−di^     here unit vector i^ are oppositely directed hence taken addition E=GMR3d+R2−d−i^ E=GMR3R2−i^ force F=E×mForce on m,  F=−GMm2R2i^