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GATE 2019 ME (ME2) – Question 15

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

A rigid equilateral triangular body PQR of unit side moves in a plane. At the shown instant QR is parallel to the x-axis, and P and R have velocities $V_P$ and $V_R$ in the x and y directions respectively. Find angular-speed magnitude.

Diagram for GATE 2019 ME (ME2) question 15
  1. $2V_R$
  2. $2V_P$
  3. $V_R/\sqrt3$
  4. $V_P/\sqrt3$

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Show answer and explanation

Correct answer: (A) $2V_R$

Explanation

The instantaneous centre is vertically below P and horizontally left of R, at the midpoint of QR. Its distance to R is 1/2. Hence $V_R=\omega/2$ and **$\omega=2V_R$, A**.