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GATE 2019 ME (ME1) – Question 40

Theory of Machines · Displacement, velocity and acceleration analysis of plane mechanisms · 2 marks · Multiple choice

The four-bar mechanism shown has AB = 5 cm, AD = 4 cm and DC = 2 cm. At this instant AB and DC are both perpendicular to AD. AB rotates at 10 rad/s. Find DC angular-speed magnitude (rad/s).

Diagram for GATE 2019 ME (ME1) question 40
  1. 0
  2. 10
  3. 15
  4. 25

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Show answer and explanation

Correct answer: (D) 25

Explanation

B and C both have horizontal velocities. Relative velocity must be perpendicular to inclined link BC, which requires their horizontal velocities to be equal. Hence $\omega_{AB}AB=\omega_{DC}DC$ and $\omega_{DC}=10(5)/2=25$ rad/s. **D**.