Two mating spur gears have $$40$$ and $$120$$ teeth respectively. The pinion rotates at $$1200$$ $$rpm$$ and transmits a torque of $$20N.m.$$ The torque transmitted by gear 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

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

Gray cast iron blocks $$200 \times 100 \times 10\,\,mm$$ are to be cast in sand moulds. Shrinkage allowance for pattern making is $$1$$%. The ratio of the volume of pattern to that of the casting will be