A taper hole is inspected using a $$CMM,$$ with a probe of $$2mm$$ diameter. At a height, $$Z=10mm$$ from the bottom, $$5$$ points are touched and a diameter of circle (not compensated for probe size) is obtained as $$20mm.$$ similarly, a $$40mm$$ diameter is btained at a height $$Z=40mm.$$ The smaller diameter (in $$mm$$) of hole at $$Z=0$$ is

What are the upper and lower limits of the shaft represented by $$60{f_8}$$?

Use the following data:
Diameter $$60$$ lies in the diameter step of $$50-80$$ $$mm$$
Fundamental tolerance unit, $$i,$$ in $$\mu m = 0.45\,\,{D^{1/3}} + 0.001D,$$
where $$D$$ is the representative size in $$mm;$$ Tolerance value for $${\rm I}T8 = 25i,$$ Fundamental deviation for $$'‘f’'$$ shaft $$ = - 5.5{D^{0.41}}$$

A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel on the taper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and the protruding portion of the mandrel surface is perfectly cylindrical. Measurement are recorded as $${R_x} = $$ maximum deflection minus minimum deflection, corresponding to sensor position at $$X$$, over one rotation.

If $${R_p} = {R_Q} > 0,$$ which one of the following would be consistent with the observation?

A hole is specified as $${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\,\,mm.$$ The mating shaft has a clearance fit with minimum clearance of $$0.01mm.$$ The tolerance on the shaft is $$0.04mm.$$ The maximum clearance in $$mm$$ between the hole and the shaft is