In a wire drawing operation, diameter of a steel wire is reduced from $$10$$ $$mm$$ to $$8$$ $$mm.$$ the mean flow stress of the material is $$400$$ $$MPa.$$ The ideal force required for drawing ignoring friction and redundant work is:

A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is $$0.1.$$ The minimum possible thickness of the sheet that can be produced in a single pass is

In a rolling process, sheet of $$25$$ $$mm$$ thickness is rolled to $$20$$ $$mm$$ thickness. Roll is of diameter $$600$$ $$mm$$ and it rotates at $$100$$ $$rpm.$$ The roll strip contact length will be

A brass billet is to be excluded from its initial diameter of $$100mm$$ to a final diameter of $$50mm$$. The working temperature is $${700^ \circ }C$$ and the extrusion constant is $$250$$ $$MPa.$$ The force required for extrusion is