In a machining operation, doubling the cutting speed reduces the tool life to $$1/{8^{th}}$$ of the original value. The exponent $$n$$ in Taylor's tool life equation $$V{T^n} = C,$$ is

A batch of $$10$$ cutting tools could produce $$500$$ components while working at $$50$$ $$rpm$$ with a tool feed of $$0.25$$ $$mm/rev$$ and depth of cut of $$1$$ $$mm.$$ A similar batch of $$10$$ tools of the same specification could produce $$122$$ components while working at $$80$$ $$rpm$$ with a feed of $$0.25$$ $$mm/rev$$ and $$1$$ $$mm$$ depth of cut. How many components can be produced with one cutting tool at $$60$$ $$rpm$$?

During orthogonal cutting of mild steel with a $$10$$ degrees rake angle tool the chip thickness ratio was obtained as $$0.4.$$ The shear angle (in degrees) evaluated from this data is

For turning $$NiCr$$ alloy steel at cutting speeds of $$64m/min$$ and $$100m/min,$$ the respective tool lives are $$15min$$ and $$12$$ $$min.$$ The tool life for a cutting speed of $$144m/min$$ is