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GATE 2016 ME (ME1) – Question 46

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

In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of 100 rpm in the counterclockwise direction, the angular speed of arm 5 (in rpm) is

Diagram for GATE 2016 ME (ME1) question 46
  1. 166.7 counterclockwise
  2. 166.7 clockwise
  3. 62.5 counterclockwise
  4. 62.5 clockwise

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Show answer and explanation

Correct answer: (C) 62.5 counterclockwise

Explanation

For sun2 and internal ring4, relative-speed relation is(N2−Na)/(N4−Na)=−Z4/Z2=−100/60. With N2=0 and N4=100rpm counterclockwise, solve−Na/(100−Na)=−5/3. This gives **Na=62.5rpm counterclockwise, C**. The planet tooth count is consistent with the geometry.