The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and included angle of the thread are 4 mm and 60°, respectively. The diameter of the best size wire is _________ mm (round off to 2 decimal places).

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

A cylindrical pin $$25_{ + 0.010}^{ + 0.020}\,\,mm$$ diameter is electroplated. Plating thickness is
$${2.0^{ \pm 0.005}}\,\,mm$$. Neglecting the gauge tolerance, the diameter (in $$mm,$$ up to $$3$$ decimal points accuracy) of the $$GO$$ ring gauge to inspect the plated pin is ___________

For the situation shown in the figure below the expression for $$H$$ in terms of $$r, R$$ and $$D$$ is