A $\backslash (400\backslash$mathrm$\{$~V$\},3-\backslash$mathrm$\{$ph$\},50\backslash$mathrm$\{$~Hz$\}\backslash ),4-$pole star connected induction motor takes a line current of $10$ A with $0\mathrm{.}8$ pf lagging. Its stator losses are $\backslash (5\backslash \%\backslash )$ of the input. Rotor Cu losses are $\backslash (4\backslash \%\backslash )$ of the input to the rotor and mechanical losses are $\backslash (3\backslash \%\backslash )$ of the input of the rotor. Calculate:

$($a$)$Slip and rotor speed

$($b$)$ Torque induced in the rotor

$($c$)$Load torque.