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

In order to test the efficiency of reducer gear train $$1kW$$ input was given at the input end at a speed of $$1440$$ $$rpm$$ and at the output end the measured torque was $$56.36$$ $$N.m.$$ If the ratio of speed reduction in this unit is $$10:1,$$ the efficiency is about