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

A block brake shows below has a free width of $$300$$ $$mm$$ and a mean coefficient of friction of $$0.25$$. For an activating force of $$400$$ $$N$$, the braking torque in $$N$$-$$m$$ is

A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a load of $$2kN$$. The lubricant used has a viscosity of $$20mPa$$-$$s$$. The radial clearance is $$50\mu m.$$ The Sommerfeld number for the bearings is

A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is doubled to $$2F$$ is