In linear gas tungsten arc welding of two plates of the same material, the peak temperature $$T$$ (in $$K$$) is given as ܶ$$T = {{{c_1}q} \over \alpha },$$ where $$q$$ is the heat input per unit length (in $$J/m$$) of weld, $$\alpha $$ is the thermal diffusivity (in $${m^2}/s$$) of the plate materials and $${C_1}$$ is a constant independent of process parameters and material types. Two welding cases are given below.

where, $$V$$ is welding voltage, $$I$$ is welding current, $$v$$ is welding speed, and $$k,$$ $$\rho $$ and $$C$$ refer to the thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider that electrical energy is completely converted to thermal energy. All other conditions remain same.

The ratio of the peak temperature in Case $${\rm I}$$ to that in Case $${\rm I}{\rm I}$$ 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 $$60$$ $$mm$$ wide block of low carbon steel is face milled at a cutting speed of $$120$$ $$m/min,$$ feed of $$0.1$$ $$mm$$/tooth and axial depth of cut of $$4$$ $$mm.$$ A schematic representation of the face milling process is shown below. The diameter of the cutter is $$120$$ $$mm$$ and it has $$12$$ cutting edges. The material removal rate (in $$m{m^3}/s)$$ 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 ________________