Cylindrical pins of diameter $${15^{ \pm 0.020}}\,\,mm$$ are being produced on a machine. Statistical quality control tests show a mean of $$14.995$$ $$mm$$ and standard deviation of $$0.004mm.$$ The process capability index $${C_p}$$ is

Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is $$20$$ $$\mu m$$ The central line average surface roughness $${R_a}$$ (in $$\mu m$$) is

Circular arc on a part profile is being machined on a vertical $$CNC$$ milling machine. $$CNC$$ part program using metric units with absolute dimensions is listed below:

$$\eqalign{ & N60\,\,\,\,G01\,\,\,\,X\,30\,\,\,\,Y\,55\,\,\,\,Z\,5\,\,\,\,F50 \cr & N70\,\,\,\,G02\,\,\,X\,50\,\,\,\,Y\,35\,\,\,\,R\,20 \cr & N80\,\,\,\,G01\,\,\,\,Z\,5 \cr} $$

The coordinates of the center of the circular arc are:

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100 e^-x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.