Torsion$($Power Transmission$)$: Example $5[5-30]$

Determine the smallest diameter of the steel shaft BC to the nearest $\frac{1}{8}$ in$.$

The motor delivers $50$ hp while turning at a constant rate of $1350$ rpm at A$.$

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=12$ksi