GATE 2022 CE (CE2) – Question 50
Two collinear rods HI and IJ, each length b=2 m, lie between fixed ends. Their axial rigidities are 2AE and AE, with AE=10⁶ N. Both have α=10⁻⁶ °C⁻¹. Only IJ is heated by ΔT=50°C. Find rightward P at I that leaves HI force zero (nearest N).
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Correct answer: 50
Explanation
Zero axial force in HI requires zero strain there. Since H is fixed, I must therefore have zero displacement. The heated rod IJ is then fully restrained against its free thermal expansion.
Its compression is $AE\alpha\Delta T=10^6(10^{-6})(50)=50$ N. It pushes I left, requiring **P=50 N** to the right.