A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varying from $$4$$ to $$8MPa.$$ Assume that the yield, ultimate and endurance strength of material are $$600,800,400MPa$$respectively. The factor of safety as per Goodman's relation is

A bolted joint in shown below. The maximum shear stress, in $$MPa,$$ in bolts $$A$$ and $$B$$ respectively are

A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a power of $$20KW$$. The teeth are on the $${20^ \circ }$$ full-depth system and have a module of $$5mm.$$ The length of the line of action is $$19mm.$$

The center distance for the above gear set in $$mm$$ is

A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a power of $$20KW$$. The teeth are on the $${20^ \circ }$$ full-depth system and have a module of $$5mm.$$ The length of the line of action is $$19mm.$$

The contact ratio of the contacting tooth is