a single rolling operation reduces a $18$mm thick plate to $15\mathrm{.}5$mm$.$ The starting plate is $200$mm wide. Roll radius $=220$ and rotational speed $=45$rev$/$mimine$.$ The work metal has a strength coefficient $=450$Mpa and a strain hardening exponent $=0\mathrm{.}17.$ Determine

$($a$)$ roll force

$($b$)$ roll torque

$($c$)$ power required for this operation