GATE 2016 ME (ME2) – Question 46
The rod AB, of length 1 m, 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 VA of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is ___________ m/s.
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Show answer and explanation
Correct answer: 0.95 to 1.05
Explanation
Take rightward x and upward y. VA=2(cos60°,sin60°)=(1,sqrt3)m/s. The rigid-rod condition (VB−VA) dot(B−A)=0, with rod direction(1/2,−sqrt3/2), gives VB=−2m/s horizontally. Midpoint velocity is the average of endpoint velocities:(−0.5,sqrt3/2), with magnitude **1m/s**.