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GATE 2019 ME (ME1) – Question 26

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

Position vector OP for P(20,10) rotates counterclockwise 30° in the XY plane to position Q shown. Find Q’s coordinates (x,y).

Diagram for GATE 2019 ME (ME1) question 26
  1. (13.40, 22.32)
  2. (22.32, 8.26)
  3. (12.32, 18.66)
  4. (18.66, 12.32)

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Show answer and explanation

Correct answer: (C) (12.32, 18.66)

Explanation

The planar rotation gives $x=20\cos30^\circ-10\sin30^\circ=12.3205$ and $y=20\sin30^\circ+10\cos30^\circ=18.6603$. Thus **(12.32,18.66), C**. The signs follow counterclockwise rotation in a fixed coordinate frame.