Engineering strain of a mild steel sample is recorded as $$0.100\% .$$ The true strain is

Spot welding of two steel sheets each $$2$$ $$mm$$ thick carried out successfully by passing $$4$$ $$kA$$ of current for $$0.2$$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $$5$$ $$mm$$ in diameter. Assuming cylindrical shape for the nugget, the thickness of the nugget is ______________$$mm.$$

For an orthogonal cutting operation, tool material is $$HSS,$$ rake angle is $${22^ \circ },$$ chip thickness is $$0.8$$ $$mm,$$ speed is $$48$$ $$m/min$$ and feed is $$0.4$$ $$mm/rev$$. The shear plane angle (in degrees) is

In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor's exponent is $$0.25.$$ If the cutting speed is reduced by $$50\% $$ then the tool life changes by ____________ times.