The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left (←) or the right (→) direction.

If the object A (Rack) is translating towards the right () direction, the correct statement among the following is

The correct option is: Object B translates towards the left direction.

Let us analyze the motion of each component in the assembly step-by-step, starting from the input motion of Object A:
1. Interaction between Object A (Rack) and Object P (Pinion):
According to the image, the top rack (Object A) translates towards the right (→). As it moves, the teeth on the bottom side of Object A push the top teeth of the meshed pinion (Object P) to the right. This forces Object P to rotate in the clockwise direction about its center.
2. Interaction between Object P and Object Q (Pinion):
Pinion Q is externally meshed with Pinion P. When two external gears mesh, they rotate in opposite directions. Therefore, the clockwise rotation of Pinion P forces Pinion Q to rotate in the anticlockwise direction.
3. Interaction between Object Q and Object R (Pinion):
Similarly, Pinion R is externally meshed with Pinion Q. Because of the opposite rotation rule, the anticlockwise rotation of Pinion Q causes Pinion R to rotate in the clockwise direction.
4. Interaction between Object R and Object B (Rack):
Pinion R is meshed at its bottom with the lower rack (Object B). As Pinion R rotates clockwise, its bottom-most teeth (which are in contact with Object B) move towards the left. This linear force pushes the rack, causing Object B to translate towards the left direction (←).