A strip with sectional area $$150mm\,\, \times \,\,4.5mm$$ is being rolled with $$20\% $$ reduction of area using $$450mm$$ diameter rollers. The angle subtended by the deformation zone at the roll center is (in radians)

A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and $$80\% $$ are available. For minimum error in the final size, the number of stages and reduction at each stage respectively would be

Calculate the bite angle when rolling plates $$12mm$$ thick using work rolls $$600mm$$ diameter and reducing the thickness by $$3mm$$