In spot pulsed laser welding of aluminium plates (density $$ = 2700kg/{m^3},$$ specific heat $$=896J/kg,$$ melting temp $$=933K,$$ latent heat of melting $$ = 398\,\,kJ/kg)$$ at a temp of $${30^ \circ }C,$$ pulse with energy of $$0.5J$$ is focused onto an area of $$0.05m{m^2}.$$ If the entire energy is coupled into the material, what will be the depth of weld assuming the $$CS$$ area of the weld is circular and is uniform throughout its depth and only heat conduction in the direction of penetration

Two different tools $$A$$ and $$B$$ having nose radius of $$0.6mm$$ and $$0.33mm$$ respectively are used to machine $$C-45$$ steel employing feed rate of $$0.2$$ $$mm/rev$$ and $$0.1mm/rev$$ respectively. The tool that gives better finish and the value of ideal surface roughness are

A cutting tool is designated in 'Orthogonal Rake System' as: $$${0^ \circ } - {0^ \circ } - {6^ \circ } - {6^ \circ } - {25^ \circ } - {75^ \circ } - 0.8\,\,mm.$$$
The following data were given
$${S_0} = $$ feed $$=0.12$$ $$mm/rev$$
$$T=$$ depth of cut $$=2.0$$ $$mm$$
$${a_2} = $$ chip thickness $$=0.22$$ $$mm$$
$${V_f} = $$ chip velocity $$=52.6$$ $$m/min$$
$${\tau _s} = $$ dynamic yield shear strength $$=400$$ $$MPa$$
$${P_z} = $$ main cutting force $$ = {S_0}\,t\,{\tau _s}\left( {\zeta \,\sec y - \tan \gamma + 1} \right)$$

Where $$\zeta = $$ chip reduction coefficient and $$\gamma = $$ orthogonal rake.
The main cutting force $$\left( {{P_z}} \right)$$ and cutting power assuming orthogonal machining are

Match GROUP - I with GROUP - II