$1.$ A shaft is designed to transmit power from a gear mounted at its right$-$end $($location B$)$ to another gear. The torque transmitted from the shaft to the gear at B through a key is given as $\backslash (\backslash$mathrm$\{$T$\}=2819\backslash$mathrm$\{$lb$\}\backslash ).$in$.$ The nominal shaft diameter at B is $1\mathrm{.}00$ in$,$ and a $0\mathrm{.}25$ in square key is recommended for a $1\mathrm{.}00$ in shaft diameter. Using a design factor of $1\mathrm{.}1,$ design an appropriate key for the gear. $($Use $1020$ CD steel for the key material$).$