A spherical hollow cavity is made in a lead sphere of radius R, such that its surface touches the outside - Physics - Gravitation

Question

A spherical hollow cavity is made in a lead sphere of radius
R, such that its surface touches the outside surface of the lead
sphere and passes through its centre The mass of the sphere before
hollowing was M With what gravitational force will the hollowed-out
lead sphere attract a small sphere of mass 'm', which lies at a
distance d from the centre of the lead sphere on the straight line
connecting the centres of the spheres and that of the hollow, if d
= 2R:

Shobhit Mittal · Accepted Answer

find the new center of mass of the lead balldensityD=M43πR3X=-43πR23DR2M-43πR23D=-43πR23M43πR3R2M-43πR23M43πR3=-MR16M-M8=-MR167M8=-R14distance of center of mass from the mass m r=2R+R14=29R14force on mass  mF=G7M8m29R142Regards