GATE ME 2016 Set 2 — Question 46
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Engineering Mechanics → Dynamics → Instantaneous Center of Rotation
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Question
The rod AB, of length , shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity of the slider at A is , the velocity of the midpoint of the rod at this instant is ___________ m/s.
Correct answer
0.95 to 1.05
Solution
In the given configuration, the paths QP and QR both make an angle of with the horizontal, meaning the angle between the two paths is . Let the intersection of the paths be O. The rod AB forms an equilateral triangle OAB at this instant because the length and the angles at O, A, and B are all . Using the Instantaneous Center of Rotation (ICR) method, the ICR of rod AB is located at a point such that the velocities and are perpendicular to the lines connecting the ICR to A and B respectively. Due to the symmetry of the equilateral triangle and the velocity directions, the velocity of the midpoint of the rod is exactly half the velocity of the slider at A. Thus, .
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