The purpose of helical grooves in a twist drill is to
$$1.$$ Improve the stiffness
$$2.$$ Save a tool material
$$3.$$ Provide space for chip removal
$$4.$$ Provide rake angle for the cutting edge

Select the correct answer suing the codes given below

Orthogonal machining of a steel work-piece is done with a $$HSS$$ tool of zero rake angle. The ratio of the cutting force and the thrust force on the tool is $$1:0.372.$$ The length of cut chip is $$4.71$$ $$mm$$ while the uncut chip length is $$10$$ $$mm.$$ What are the shear plane angle $$\phi $$ and friction angle $$\beta $$ in deg.? Use Merchant's theory.

A single point cutting tool with a nose radius of $$0.4$$ $$mm$$ was used to turn a component in a lathe employing a feed rate of $$0.3$$ $$mm/rev.$$ If the feed-rate is doubled, the ideal surface roughness (peak-to-valley height) produced on the component will increase by a factor of

Tool life equation for two tools under consideration are as follows

$$\eqalign{ & HSS:\,\,\,\,\,\,\,\,\,\,\,\,\,V{T^{0.2}} = 150 \cr & Carbide:\,\,\,\,\,\,V{T^{0.3}} = 250 \cr} $$
Where $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in $$min.$$ The breakdown cutting speed above which the carbide tool will be beneficial is