A one piece, solid steel gear $+$ shaft component is being loaded by a gear tooth force, FT$,$ as shown

with the dimensions in the diagram below. This gear shaft is being supported at each end $($ A and B

with a ball bearing. A moment load at point B reacts the gear tooth force FT$.$ Ignore the thickness

of the gear blank $($disc$).$ The material is ductile, high strength steel with a Yield Strength of $100$

ksi.

Find: The factor of safety at gear $C.$