In a single-pass rolling operation, a $$200$$ $$mm$$ wide metalic strip is rolled from a thickness $$10$$ $$mm$$ to a thickness $$6$$ $$mm.$$ The roll radius is $$100$$ $$mm$$ and it rotates at $$200$$ $$rpm$$. The roll-strip contact length is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in plane strain of the strip material in the roll gap is $$500$$ $$MPa$$, the roll separating force (in $$kN$$) is _________________

Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to create the same percentage reduction in their respective heights. Consider that the die-work-piece interface friction is negligible. The ratio of the final diameter of the shorter cylinder to that of the longer cylinder is _________________.

The ratio of press force required to punch a square hole of $$30$$ $$mm$$ side in a $$1$$ $$mm$$ thick aluminium sheet to that needed to punch a square hole of $$60$$ $$mm$$ side in a $$2$$ $$mm$$ thick aluminium sheet is________.

The limits of a shaft designated as $$100h5$$ are $$100.000$$ $$mm$$ and $$100.014$$ $$mm.$$ Similarly, the limits of a shaft designated as $$100h8$$ are $$100.000$$ $$mm$$ and $$100.055$$ $$mm.$$ If a shaft is designated as $$100h6,$$ the fundamental deviation (in $$\mu m$$ ) for the same is