Two elastic rods are joined between fixed supports as shown in the figure. The condition for no change in the lengths of individual rods with the increase of temperature is: (α₁α₂ = linear expansion coefficient, A₁ A₂ = area of rods, Y₁Y₂ = Young's modulus)
Correct answer: D. D
- A. A
- B. B
- C. C
- D. D
Explanation
The correct condition for no change in the lengths of theindividual rods when the temperature increases is given bythe equation A1Y1α1 = A2Y2α2. This equation ensures thatthe forces due to thermal expansion in both rods arebalanced. If this condition is met, the rods will notexperience any net change in length, as the expansion ofone rod will be perfectly countered by the expansion of theother.Other options fail to correctly balance these forces becausethey either swap the Young's modulus values, ignore thecross-sectional area, or omit the Young's modulusaltogether, leading to an incorrect assessment of the forces involved.
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