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. The assembly (from the figure): Pinion 1 meshes with Rack 1 on top and Rack 2 below. Pinion 2 meshes with Rack 2. Pinion 3 meshes with Rack 2. Rack 1 is on top, Rack 2 is in the middle between pinions. If the object A (Rack) is translating towards the right (+) direction, the correct statement among the following is: A. Object B translates towards the right direction. B. Object B translates towards the left direction. C. Object C rotates in the anti-clockwise direction. D. Object C rotates in the clockwise direction.

GATE 2024 · General Aptitude · Image Rotation · medium

Answer: When Rack A translates to the right, Rack B (object B) translates to the left. Answer: B.

  1. Rack A moves right => Pinion 1 rotates clockwise: Rack A is on the top of Pinion 1. Rack A moves right (+). By the rack-pinion meshing rule, the top of Pinion 1 is dragged to the right, so Pinion 1 rotates clockwise (CW).
  2. Pinion 1 rotates CW => Rack B (bottom rack) moves left: Rack B is in contact with the bottom of Pinion 1. Pinion 1 rotates CW, so its bottom moves to the left. Therefore Rack B is pushed to the left (-) direction.
  3. Rack B moves left => Pinion 2 rotates counter-clockwise (CCW): Rack B is also on the top of Pinion 2. Rack B moves left (-). By the rack-pinion rule, the top of Pinion 2 moves left => Pinion 2 rotates CCW.
  4. Evaluate the answer options: A. Object B translates right: WRONG (we found B goes left). B. Object B translates left: CORRECT. C. Object C (Pinion 3 or Pinion 2) rotates CCW: if object C = Pinion 2, it rotates CCW => this could also be correct depending on labeling. D. Object C rotates CW: WRONG if C = Pinion 2. Since the official answer is B (from the answer key), and the direct chain shows Rack B moves left, option B is confirmed correct.