Project ForgeCylindrical bars P and Q have identical lengths and radii but different linear elastic materials, perfectly bonded at the interface, with Q's Young's modulus and coefficient of thermal expansion both twice P's corresponding values. The bars are held between rigid supports and the temperature is raised by ΔT. Denote the magnitudes of stress in P and Q by σ1 and σ2 respectively. Which of the statement(s) given is/are CORRECT?
- The interface between P and Q moves to the left after heating
- BThe interface between P and Q moves to the right after heating
- Cσ1 < σ2
- σ1 = σ2
Explanation
Since P and Q form a single series bar between two rigid (fixed) walls with equal cross-sectional area, the same internal axial force N is transmitted through both segments at every cross-section (equilibrium of a series member with no external load along its length) — so σ1=N/A=σ2=N/A always, regardless of the differing E and α (option D correct, C wrong). Tracking the interface's own displacement (via bar P's free thermal expansion minus its force-induced compression) gives a net displacement of −αP·ΔT·LP relative to its original position — i.e. the interface moves toward the P-side wall (LEFT) after heating (option A correct, B wrong).
Source: GATE ME 2023 Official Paper (2023)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.