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GATE 2018 ME (ME2) – Question 40

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 2 marks · Multiple choice

The shown rigid rod of length 1 m rests at θ = 45°. End P is dragged right at U = 5 m/s. Find the magnitude of Q’s velocity V (m/s) as it moves along the wall without losing contact.

Diagram for GATE 2018 ME (ME2) question 40
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Correct answer: (A) 5

Explanation

The rod endpoints satisfy $x^2+y^2=L^2$. Differentiating gives $x\dot x+y\dot y=0$, so downward speed magnitude is $V=(x/y)U$. At 45°, x = y; therefore **V = 5 m/s, A**.