$12.(8$ points$)$ Two identical spheres, each of mass $3$ kg and radius $0\mathrm{.}05$ m $,$ are hung from their centers with $0\mathrm{.}2$ m long strings. The strings are fixed to the same spot on a platform above the two spheres. The platform, strings and spheres all begin to rotate with a very slowly increasing rate of rotation.

$($a$)$ Draw a free body diagram for the left sphere. Draw the diagram assuming the apparatus is spinning, but the balls are still in contact $($see part b$).$ Each force should be labeled, in an appropriate direction. If there is$,$ or is not, a net force in a direction, scale the forces to reflect this.

$($b$)$ As the apparatus spins faster, the two sphere's will lose contact with each other. At what $($linear$)$ speed are the balls travelling when this happens? Hint: what happens to the normal force between the spheres when they lose contact?