The solid shafts $\frac{?}{\text{b}\text{a}\text{r}}(ABC)$ and $\frac{?}{\text{b}\text{a}\text{r}}(DEF)$ and the gears shown are used to transmit $25$ hp from the motor $"M"$ to a machine tool connected to shaft DEF. Knowing that the motor rotates at $1200$ rpm and that ${}_{\text{a}\text{l}\text{l}}=7\mathrm{.}0$ksi.

$1)$Determine the bending moment at point $"$B$",M_B($lb$-$in$).$

$2)$Determine the minimum diameter,$d_{\text{m}\text{i}\text{n}},$ for the shaft ABC, to the nearest $1/8$in$.$