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GATE 2020 ME (ME2) – Question 16

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 1 mark · Multiple choice

A circular disc of radius r rolls without slipping at contacts P and Q with two plates. The upper plate moves left at v and the lower right at 2v. Find the magnitude of the disc’s angular velocity.

Diagram for GATE 2020 ME (ME2) question 16
  1. $v/r$
  2. $v/(2r)$
  3. $2v/(3r)$
  4. $3v/(2r)$

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Show answer and explanation

Correct answer: (D) $3v/(2r)$

Explanation

Take right positive and counterclockwise ω positive. Top velocity is U−ωr=−v, bottom velocity U+ωr=2v. Subtracting gives2ωr=3v, so **ω=3v/(2r), D**. Adding also gives centre speed U=v/2.