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

Twenty degree full depth involute profiled $$19$$-tooth pinion and $$37$$-tooth gear are in mesh. If the module is $$5mm,$$ the center distance between the gear pair will be

A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arrangement. The input gear is mounted on the motor shaft. The gears have involutes teeth of $$2$$ $$mm$$ module.

If the drive efficiency is $$80\% ,$$ the torque required on the input shaft to create $$1000N$$ output thrust is

A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arrangement. The input gear is mounted on the motor shaft. The gears have involutes teeth of $$2$$ $$mm$$ module.

If the pressure angle of the rack is $${20^ \circ },$$ the force acting along the line of action between the rack and the gear teeth is