Q$1(25\%)$ A $200\backslash$times $15$ mm strip is fed through a rolling mill with two powered rolls each of $180$ mm radius. The work thickness is to be reduced to $12$ mm at a roll speed of $60$ rpm $.$ The flow stress of work material is $85$ MPa and the coefficient of frietion between roll and work is about $0\mathrm{.}11.$ Determine:

a$)$ Is the friction sufficient to permit rolling operation in one pass?

b$)$ Number of pass to accomplish the operation

c$)$ Speed of no slip point

d$)$ The roll force, torque and horsepower