The center-to-center distance between a \(200 \mathrm{~g}\) lead sphere and an \(800 \mathrm{~g}\) lead sphere is \(0.120 \mathrm{~m}\). A \(1.00 \mathrm{~g}\) object is placed \(0.0800 \mathrm{~m}\) from the center of the \(800 \mathrm{~g}\) sphere along the line joining the centers of the two spheres.

(a) Ignoring all sources of gravitational force except the two spheres, calculate the gravitational force exerted on the object.

(b) Determine the gravitational potential energy per gram at the position of the object.

(c) How much work is needed to keep the object from getting closer than \(0.0400 \mathrm{~m}\) from to the \(800 \mathrm{~g}\) sphere?