In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor's exponent is $$0.25.$$ If the cutting speed is reduced by $$50\% $$ then the tool life changes by ____________ times.

For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is a constant, $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in minutes. The Taylor's tool life equation is $$V{T^{0.25}} = 150.$$ The cutting speed (in $$m/min$$) for the minimum total cost is ___________

The too life equation for $$HSS$$ tool is $$V{T^{0.14}}\,\,{f^{0.7}}\,\,{d^{0.4}} = $$ Constant. The tool life $$(T)$$ of $$30$$ $$min$$ is obtained using the following cutting conditions $$=45$$ $$m/min,$$ $$f=0.35mm,$$ $$d=2.0$$ $$mm.$$ If speed $$(V),$$ feed $$(f)$$ and depth of cut $$(D)$$ are increased individually by $$25\% ,$$ the tool life (in $$min$$) is

Orthogonal turning of a mild steel tube with a tool of rake angle $${10^0}$$ is carried out at a feed of $$0.14$$ $$mm/rev.$$ If the thickness of the chip produced is $$0.28mm,$$ the values of shear angle and shear strain will be respectively.