$5-49$ Cantilevered rod $\backslash ($ O A $\backslash )$ is $0\mathrm{.}5$ m long, and made from AISI $1010$ hot$-$rolled steel. A constant force and torque are applied as shown. Determine the minimum diameter, $\backslash ($ d $\backslash ),$ for the rod that will achieve a minimum static factor of safety of $2$

$($a$)$ using the maximum$-$shear$-$stress failure theory.

$($b$)$ using the distortion$-$energy failure theory.