$($b$)$ It is found in a laboratory cold rolling experiment that a plate of $6$ mm cannot be reduced to less than $3$ mm in a single pass. In the above two$-$high experimental rolling mill, both the rollers are rigid $($no deflection of rollers$)$ and the diameter of both these rollers are $300$ mm $.$ Also, these rollers are rotating uniformly at $300$ RPM$.$ Assume that the deformation is under plane strain condition and the plate is a rigid perfectly plastic material with uniaxial tensile yield strength of $300$ MPa $.$ Evaluate the coefficient of friction at the sheet and roller interface.