A rod of length $$20$$ $$mm$$ is stretched to make a rod of length $$40$$ $$mm.$$ Subsequently, it is compressed to make a rod of final length $$10$$ $$mm.$$ Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

A strip of $$120mm$$ width and $$8mm$$ thickness is rolled between two $$300$$ $$mm$$-diameter rolls to get a strip of $$120mm$$ width and $$7.2mm$$ thickness. The speed of the strip at the exit is $$30m/min.$$ There is no front or back tension. Assuming uniform roll pressure of $$200$$ $$MPa$$ in the roll bite and $$100\% $$ mechanical efficiency, the minimum total power (in $$kW$$) required to drive the two rolls is ____________________

A $$300$$ $$mm$$ thick slab is being cold rolled ussing roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______

A $$300$$ $$mm$$ thick slab is being cold rolled using roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______________