A single – plate clutch has a friction disc with inner and outer radii of $$20mm$$ and $$40$$ $$mm,$$ respectively. The friction lining in the disc is made in such a way that the coefficient of friction $$\mu $$ varies radially as $$ = 0.01\,r,$$ where $$r$$ is in $$mm.$$ The clutch needs to transmit a friction torque of $$18.85$$ $$kN.mm.$$ As per uniform pressure theory, the pressure (in $$MPa$$) on the disc is ___________________.

It is desired to make a product having T-shaped cross - section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

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 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