A $6$ pole, $50$ Hz$,3$ phase induction motor running on full load develops a useful torque of $150$ N$.$m at a rotor frequency of $1\mathrm{.}5$Hz$.$ Calculate the shaft power output, if the mechanical torque lost in friction be $10$ N$.$m$,$ determine $($a$)$ rotor copper loss, $($b$)$ the input to the motor, and $($c$)$ the efficiency. The total stator loss is $700$ watt.