A $40$Kw$,3--$connected $50$ HZ $415$V cylindrical motor synchronous motor operates at the condition

with a $0\mathrm{.}8$pf leading. The motor efficiency excluding field and stator loss is $94\%$ and Xs $=2.$

Calculate

i$)$ Mechanical power developed

ii$)$ Armature current

iii$)$ Back emf

iv$)$ Power angle

v$)$ Maximum or pull out torque of the motor