The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$
When $$\varepsilon $$ is true strain. The Young's modulus of elasticity of the material is $$200$$ $$GPa.$$ A block of thickness $$100$$ $$mm$$ made of this material is compressed to $$95$$ $$mm$$ thickness and then the load is removed. The final dimension of the block (in $$mm$$) is ____________

A metal rod of initial length $${L_0}$$ is subjected to a drawing process. The length of the rod at any instant is given by the expression, $$L\left( t \right) = {L_0}\left( {1 + {t^2}} \right),$$ where $$t$$ is the time in minutes. The true strain rate (in $${\min ^{ - 1}}$$) at the end of one minute is _____________

A mild steel plate has to be rolled in one pass such that the final plate thickness is $$2/{3^{rd}}$$ of the initial thickness, with the entrance speed of $$10m/min$$ and roll diameter of $$500mm.$$ If the plate widens by $$2\% $$ during rolling, the exit velocity (in $$m/min$$) is ____________

In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$$ undergoes $$10\% $$ reduction of thickness. The angle of bite in radians is