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GATE 2016 ME (ME3) – Question 19

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

A rigid link PQ is undergoing plane motion as shown in the figure (VP and VQ are non-zero). VQP is the relative velocity of point Q with respect to point P. Which one of the following is TRUE?

Diagram for GATE 2016 ME (ME3) question 19
  1. VQP has components along and perpendicular to PQ
  2. VQP has only one component directed from P to Q
  3. VQP has only one component directed from Q to P
  4. VQP has only one component perpendicular to PQ

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Correct answer: (D) VQP has only one component perpendicular to PQ

Explanation

Rigid-body kinematics gives v_B−v_A=ω×r_BA. A cross product is perpendicular to the separation vector, so the relative velocity is perpendicular to the line joining the points. Hence **D**. Their absolute velocities need not be perpendicular to that line.