$2.$ Draw the end view of flat rolling process and prove that $\backslash ($ L$=\backslash$sqrt$\{$R$\backslash$left$($h$\_\{$o$\}-$h$\_\{$f$\}\backslash$right$)\}\backslash ).$

$3.$ An $\backslash (1100-\backslash$mathrm$\{$O$\}\backslash )$ aluminum strip $228$ mm wide and $25$ mm thick is rolled to a thickness of $20$ mm in one pass. The roll radius is $200$ mm $,$ and the rolls rotate at $100$ rpm $.$ Calculate the roll force and the power required in this operation.

$4.$ Calculate the individual drafts in each of the stands in the tandem$-$rolling operation shown in the following figure.