GATE 2020 PI – Question 38
General Engineering · Applied Mechanics · 2 marks · Multiple choice
Two hinged bars PR and QR make angles α and β with the vertical and support weight W at joint R. Find tension in QR.
- $W\sin\beta/\cos(\alpha+\beta)$
- $W\cos\beta/\sin(\alpha+\beta)$
- $W\cos\alpha/\cos(\alpha+\beta)$
- $W\sin\alpha/\sin(\alpha+\beta)$
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Show answer and explanation
Correct answer: (D) $W\sin\alpha/\sin(\alpha+\beta)$
Explanation
Horizontal equilibrium gives TP sinα=TQ sinβ. Vertical equilibrium is TP cosα+TQ cosβ=W. Eliminate TP to obtain TQ[sinβ cosα+cosβ sinα]=W sinα, hence TQ=W sinα/sin(α+β), D.
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