GATE 2023 AR — Architecture – Question 64
A 5.65 mm diameter steel wire is 50 m long and carries a 200 kg mass. With E=2×10⁵ N/mm² and g=10 m/s², find elongation in mm, rounded to two decimal places.
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Correct answer: 19.75 to 20.15
Explanation
Load F=200×10=2000 N; length L=50000 mm. Cross-section A=π(5.65)²/4=25.0721 mm². Axial extension FL/(AE)=2000×50000/(25.0721×200000)=19.94 mm. Use consistent millimetre units with the supplied elastic modulus.