GATE 2016 ME (ME3) – Question 42
A rigid rod AB of length $L=\sqrt2$ m undergoes translation and rotation in the x–y plane as shown. End A has $\mathbf V_1=\hat i+2\hat j$ m/s. End B moves only in the x direction. The magnitude of its velocity V₂ is ______ m/s. The rod is at 45° to the positive x direction.
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Correct answer: 2.9 to 3.1
Explanation
The end separation is(1,1)m because the length is√2m at45°. Rigidity requires(v_B−v_A)·r_BA=0. With v_A=(1,2) and v_B=(v,0), this becomes(v−1)−2=0, giving **v=3m/s**. The relative velocity is normal to the rod.