A $3-$phase $400$v $50$HZ $6$pole cage inducation motor of rating $20$ KW $,$with slip at $4\%$ of the rated load $,$has a starting torque equal to $120\%$of the rated torque $.$The motor is coupled to a pump through a reducation gearbox of effieciency $85\%.$The breakaway torque is $24$ N$.$m at the motor shaft $.$Assume that the torque available fir acceleration remains constant for the entire duration and the motor accelerates to the rated spewd in $7$ seconds

a$)$ what is the rated speed of the motor

d$)$ what is the total moment of inertia of the rotating parts of the system seen at the motor shaft