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GATE 2016 CE (CE1) – Question 39

Solid Mechanics · Transformation of stress, Mohr circle · 2 marks · Multiple choice

The magnitudes of vectors P, Q and R are 100 kN, 250 kN and 150 kN, respectively as shown in the figure. The respective values of the magnitude (in kN) and the direction (with respect to the x-axis) of the resultant vector are

Diagram for GATE 2016 CE (CE1) question 39
  1. 290.9 and 96.0°
  2. 368.1 and 94.7°
  3. 330.4 and 118.9°
  4. 400.1 and 113.5°

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Correct answer: (C) 330.4 and 118.9°

Explanation

Resolve each vector into horizontal and vertical components using its angle from the positive horizontal axis. Sum Rx=100cos60°+250cos105°+150cos195° and Ry=100sin60°+250sin105°+150sin195°. Magnitude sqrt(Rx²+Ry²) is approximately330.4, and atan2(Ry,Rx) gives118.9°. This matches **C**.