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GATE 2019 ME (ME2) – Question 46

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

The shown slider-crank rotates counterclockwise at constant angular speed ω. Crank length is r. By exact analysis, find slider acceleration in the indicated y-direction at the shown instant when the crank is parallel to x.

Diagram for GATE 2019 ME (ME2) question 46
  1. $-\omega^2r$
  2. $2\omega^2r$
  3. $\omega^2r$
  4. $-2\omega^2r$

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Show answer and explanation

Correct answer: (C) $\omega^2r$

Explanation

The crank pin has vertical velocity $\omega r$ and horizontal inward acceleration $-\omega^2r$. The connecting rod has zero instantaneous angular speed because both endpoint velocities are vertical. Its angular acceleration provides the horizontal relative acceleration. With the shown 45° rod, the associated vertical component is $+\omega^2r$. Thus slider acceleration is **$+\omega^2r$, C**.