Problem $2$

Two solid steel shafts $(G=77$GPa $)$ are connected by the gears $B$ and $C.$ Shaft $CD$ is subjected to a torque of magnitude $T=1000N$ m at $D$ as shown in figure. Knowing that the diameter of shaft $AB$ is $56$ mm $,$ the diameter of shaft $CD$ is $42$ mm $,$ the radius of gear $B$ is $10$ cm $,$ the radius of gear $C$ is $4$ cm $,$ determine:

a$)$ The shear stress in shaft $CD$

b$)$ The shear stress in shaft $AB$

c$)$ The angle of twist of the end D