GATE 2017 ME (ME2) – Question 48
A uniform rod PQ of length $\sqrt2$ m and mass 10 kg is released from rest as shown. Its ends slide on frictionless faces OP and OQ. Take g = 10 m/s² and centre-of-mass inertia $ML^2/12$. Its instantaneous angular-acceleration magnitude is ______ rad/s².
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Show answer and explanation
Correct answer: 7.25 to 7.75
Explanation
Let θ be rod angle to the floor. Its centre has coordinates(L cosθ/2,L sinθ/2), so kinetic energy is ML²θ-dot²/8+ML²θ-dot²/24=ML²θ-dot²/6. Potential energy is MgL sinθ/2. At release, Lagrange equation gives |θ-double-dot|=3g cosθ/(2L). For L=√2 and θ=45°, this is **7.5rad/s²**.