$3\mathrm{.}21$ Two solid steel shafts are connected by the gears shown. A torque

of magnitude $T=900N*m$ is applied to shaft $AB.$ Knowing that the allow$-$

able shearing stress is $5$ MPa and considering only stresses due to twisting,

determine the required diameter of $($a$)$ shaft $AB,(b)$ shaft $CD.$

Fig. P$3\mathrm{.}21$ and P$3\mathrm{.}22$