A $440$ V$,1250$ rpm separately excited dc motor draws an armature current of $30$ A when delivering a rated torque of $85$ N$.$m to the load. The armature resistance is $1.$ Consider that the rotational losses $($core $+$ mechanical$)$ are proportional to the speed. Neglect the field winding losses. The field current is kept constant and the machine is not saturated. The no$-$load shaft speed is $1350$ rpm$.$ A$)$ What is the induced torque at no$-$load? B$)$ How much power is consumed by the dc motor operating at no$-$load?