A cast iron block of $$200$$ $$mm$$ length is being shaped in a shaping machine with a depth of cut of $$4$$ $$mm,$$ feed of $$0.25$$ $$mm/stroke$$ and the tool principal cutting edge angle of $${30^ \circ }.$$ Number of cutting strokes per minutes is $$60.$$ Using specific energy for cutting as $$1.49J/m{m^3},$$ the average power consumption (in Watt) is ___________

Two separate slab milling operations, $$1$$ and $$2,$$ are performed with identical milling cutters. The depth of cut in operation $$2$$ is twice that in operation $$1.$$ The other cutting parameters are identical. The ratio of maximum uncut chip thicknesses in operations $$1$$ and $$2$$ is ___________

A $$GO-No$$ $$GO$$ plug gauge is to be designed for measuring a hole of nominal diameter $$25$$ $$mm$$ with a hole tolerance of $$ \pm 0.015\,\,mm.$$ Considering $$10\% $$ of work tolerance to be the gauge tolerance and no wear condition, the dimension (in $$mm$$) of the $$GO$$ plug gauge as per the unilateral tolerance system is

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is ________