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GATE 2024 EE GA Q.9: solution and answer

GATE 2024 · EEGA Q.9 · 2 marks · MCQ

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.

[Figure]

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

GATE 2024 EE GA question 9: Black silhouette drawing of a gear train.Tap to open full size
Figure from the GATE 2024 EE paper. It is part of the question.
Figure description

Black silhouette drawing of a gear train. At the top is a horizontal rack labelled "Object A", with its teeth pointing downward and an arrow beside the label pointing to the right (→). Directly below Object A, meshing with its teeth, is the largest gear, "Object P" (label to its right). Down and to the left of P, meshing with P, is a medium gear, "Object Q" (label to its left). Below Q and slightly to the right, meshing with Q, is a smaller gear, "Object R" (label to its right). P and R do not touch. At the bottom is a horizontal rack labelled "Object B" (label below it), with its teeth pointing upward, meshing with R from underneath. So the order of contact is A (rack, on top of P) → P → Q → R → B (rack, under R).

  1. (A)

    Object B translates towards the right direction.

  2. (B)

    Object B translates towards the left direction.

  3. (C)

    Object R rotates in the anticlockwise direction.

  4. (D)

    Object Q rotates in the clockwise direction.

Answer and solution

ANSWER

(B) Object B translates towards the left direction.

Official answer: BSource: Official answer key, GATE 2024 EE (IISc Bengaluru)

  1. Read the order of contact off the figure. A meshes with the top of P, P with Q, Q with R, and R with the top of B. P and R do not touch, so the motion passes along a single chain: A → P → Q → R → B.

  2. Rack on top of a pinion: the teeth in contact move together, so the top of P moves right along with A. A wheel whose top moves right turns clockwise, so P turns clockwise.

  3. Two meshing gears turn in opposite directions. P turns clockwise, so Q turns anticlockwise. That rules out (D).

  4. Apply the same rule again. Q turns anticlockwise, so R turns clockwise. That rules out (C).

  5. Rack under a pinion: B moves with the bottom of R. When a wheel turns clockwise its bottom point moves left, so B translates to the left. That rules out (A).

  6. Quick check by counting. Each gear-to-gear mesh reverses the direction of rotation. There are 2 such meshes between the racks (P–Q and Q–R), an even number, so R turns the same way as P (clockwise). A touches the top of its gear and B touches the bottom, and the top and bottom of one wheel move in opposite directions. So A moving right means B moves left. The answer is option (B).

KEY IDEA

Meshing gears turn in opposite directions. A rack moves with the point of the pinion it touches: the top of a clockwise wheel moves right and its bottom moves left. Follow the one chain of contacts from A to B: P clockwise, Q anticlockwise, R clockwise, so B moves left.

WATCH OUT FOR

The usual slip is to count only the gear-to-gear meshes (two, so R turns the same way as P) and then say B moves the same way as A. That misses the extra reversal from A sitting on top of its pinion while B sits underneath its pinion. Another slip is to assume P and R mesh directly because they sit close together in the drawing. They do not touch, so the motion has to go through Q.

From the GATE 2024 EE paper. Every question of this paper · Download the full paper · All 23 Spatial questions, with notes

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