Two flat steel sheets, each of $$2.5$$ $$mm$$ thickness, are being resistance spot welded using a current of $$6000$$ $$A$$ and weld time of $$0.2$$ $$s.$$ The contact resistance at the interface between the two sheets is $$200\,\,\mu \Omega $$ and the specific energy to melt steel is $$10 \times {10^9}\,\,J/{m^3}.$$ A spherical melt pool of diameter $$4$$ $$mm$$ is formed at the interface due to the current flow. Consider that electrical energy is completely converted to thermal energy. The ratio of the heat used for melting to the total resistive heat generated is _____________

A helical gear with involute tooth profile has been machined with a disc-type form gear milling cutter. The helical gear has $$30$$ teeth and a helix angle of $${30^ \circ }$$. The module of the gear milling cutter is $$2.$$ The pitch circle diameter (in $$mm$$) of the helical gear is _______.

A cylindrical bar of $$100$$ $$mm$$ diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of $$120$$ $$m/min$$, $$0.25$$ $$mm/rev$$ and $$4$$ $$mm,$$ respectively. The specific cutting energy of the work material is $$1 \times {10^9}\,\,J/{m^3}.$$ Neglect the contribution of feed force towards cutting power. The main or tangential cutting force (in $$N$$) is __________________

A single point right handed turning tool is used for straight turning. The feed is $$0.25$$ $$mm/rev$$ and the uncut chip thickness is found to be $$0.25$$ $$mm.$$ The inclination angle of the main cutting edge is $${10^ \circ }.$$ The back rake angle (in degrees) is ________________