A cylindrical blind riser with diameter $$d$$ and height $$h,$$ is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio $$h:d$$ is

For spot welding of two steel sheets (base metal) each of $$3$$ $$mm$$ thickness, welding current of $$10000$$ $$A$$ is applied for $$0.2$$ $$s$$. The heat dissipated to the base metal is $$1000J.$$ Assuming that the heat required for melting $$1m{m^3}$$ volume of steel is $$20J$$ and interfacial contact resistance between sheets is $$0.0002$$$$\Omega $$, the volume (in $$m{m^3}$$) of weld nugget is _____________

A straight turning operation is carried out using a single point cutting tool on an $$AISI$$ $$1020$$ steel rod. The feed is $$0.2$$ $$mm/rev$$ and the depth of cut is $$0.5$$ $$mm.$$ The tool has a side cutting edge angle of $${60^ \circ }.$$ The uncut chip thickness (in $$mm$$) is _______________

Cutting tool is much harder than the work piece. Yet the tool wears out during the tool-work interaction, because