Two cutting tools are being compared for a machining operation. The tool life equations are:
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,Carbi{\mathop{\rm de}\nolimits} \,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,V{T^{1.6}} = 3000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,HSS\,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,V{T^{0.6}} = 200 \cr} $$

Where $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in $$min.$$ The carbide tool will provide higher tool life if the cutting speed in $$m/min$$ exceeds

A single-point cutting tool with $${12^0}$$ rake angle is used to machine a steel work-piece. The depth of cut, $$i.e$$ uncut thickness is $$0.81$$ $$mm.$$ The chip thickness under orthogonal machining condition is $$1.8$$ $$mm.$$ The shear angle is approximately

For tool $$A,$$ Taylor’s tool life exponent $$(n)$$ is $$0.45$$ and constant $$(K)$$ is $$90.$$ Similarly for tool $$B,$$ $$n=0.3$$ and $$K=60.$$ The cutting speed (in $$m/min$$) above which tool $$A$$ will have a higher tool life than tool $$B$$ is

In a machining experiment, tool life was found to vary with the cutting speed in the following manner

What is percentage increase in tool life when the cutting speed is halved.