Match the following criteria of material failure, under biaxial stresses $${\sigma _1}$$and $${\sigma _2}$$ and yield stress $${\sigma _y}$$ with their corresponding graphic representations:
$$P.$$ Maximum normal stress criterion
$$Q.$$ Maximum distortion energy criterion
$$R.$$ Maximum shear stress criterion

Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the life of bearing $$P$$ to the life of bearing $$Q$$ is

A cubic casting of $$50mm$$ side undergoes volumetric solidification shrinkage and volumetric solid contraction of $$4\% $$ and $$6\% $$ respectively. No riser is used. Assume uniform cooling in all directions. The side of cube after solidification and contraction is

Green sand mould indicates that