Two identical $400-mm-$diameter steel rollers of a rolling mill are pressed together with a force per length of $2M\frac{N}{m}.$ Using $E=200$ GPa and $v=0\mathrm{.}3,$ compute the $($a$)$ maximum contact pressure $($in MPa $)$ and $($b$)$ width of contact $($in mm $).$ Additionally, using the plot shown, estimate the value of the $($c$)$ maximum shear stress $($ In MPa$)$ at the center of the contact patch $)=(0.$