Required information

Two solid steel shafts are connected by the gears shown. A torque of magnitude $\backslash ($ T$=840\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}\backslash )$ is applied to shaft $\backslash ($ A B $\backslash ).$ The allowable shearing stress is $50$ MPa $.$

Considering only stresses due to twisting, determine the required diameter of shaft $\backslash ($ A B $\backslash ).$

The diameter of shaft $\backslash ($ A B $\backslash )$ is mm $.$