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GATE 2021 ME (ME2) – Question 42

Theory of Machines · Gears and gear trains · 2 marks · Multiple choice

A power transmission mechanism consists of a belt drive and a gear train as shown in the figure. Diameters of pulleys of belt drive and number of teeth ($T$) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are

Open belt from the 150 mm input pulley at 2500 rpm to the 250 mm pulley, followed by the labelled compound gear train. See the attached source image.
  1. 255.68 rpm clockwise
  2. 255.68 rpm anticlockwise
  3. 575.28 rpm clockwise
  4. 575.28 rpm anticlockwise

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Show answer and explanation

Correct answer: (A) 255.68 rpm clockwise

Explanation

The open belt gives $N_2=2500(150/250)=1500$ rpm. The compound gears give $N_7=1500(18/44)(15/36)=255.6818$ rpm; the idler tooth count cancels.

Three external gear meshes reverse direction three times. The shown input is anticlockwise, so output is clockwise. **Answer: A**.