Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with $$15$$ $$mm$$ diameter. The size of the moulds are such that the outside temper-ature of the moulds do not increase appreciably beyond the atmospheric temperature during solidification. The sequence of solidification in the mould from the fastest to slowest is

(Thermal conductivities of steel, copper and aluminum are $$60.5, 401$$ and $$237$$ $$W/m$$-$$K,$$ respectively. Specific heats of steel, copper and aluminum are $$434, 385$$ and $$903$$ $$J/kg$$-$$K,$$ respectively. Densities of steel, copper and aluminum are $$7854, 8933$$ and $$2700$$ $$kg/{m^3},$$ respectively.)

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.