A $$\phi $$ $$40$$ $$mm$$ job is subjected to orthogonal turning by a $$ + {10^ \circ }$$ rake angle tool at $$500$$ $$rev/min.$$ By direct measurement during the cutting operation, the shear angle was found equal to $${25^ \circ }.$$

The velocity (in $$m/min$$) with which the chip flows on the tool face is

The following data relate to an orthogonal turning process:
$$\,\,\,\,\,\,\,\,\,\,\,$$Back rake angle $$=15deg,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Width of cut $$=2mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Chip thickness $$=0.4mm,$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Feed rate $$=0.2mm/rev.$$

If the cutting force and the thrust force are $$900N$$ and $$810N,$$ the mean strength in $$Mpa$$

Consider the following statements
$$1.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ As the cutting speed increases, the cost of production initially reduces, then
$$\,\,\,\,\,\,\,\,\,\,\,\,$$after an optimum cutting speed it increases.
$$2.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ As the cutting speed increases the cost of production also increases and
$$\,\,\,\,\,\,\,\,\,\,\,\,$$after a critical value to it reduces.
$$3.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ Higher feed rate for the same cutting speed reduces cost of production.
$$4.$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ Higher feed rate for the same cutting speed increases the cost of production

Which of the statements given above are correct?

The rake angle of a cutting tool is $${15^ \circ }$$, shear angle $${45^ \circ }$$ and cutting velocity $$35$$ $$m/min$$. What is the velocity of chip along the tool face?