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A composite rod consists of a steel segment (length 25 cm, cross-sectional area 2A) and a copper segment (length 50 cm, cross-sectional area A) joined end to end. An axial load F is applied. The Young's modulus of steel to copper is 2:1. Which of the following statements are INCORRECT?
- The extension produced in the copper rod will be more.
- The extensions in the copper and steel parts are in the ratio 2:1.
- The stress applied to the copper rod will be more.
- No extension will be produced in the steel rod.
Correct answer: The extensions in the copper and steel parts are in the ratio 2:1.
Solution
Both segments carry force F. Yₛ = 2*Y_c. deltaₛ = F*Lₛ/(Aₛ*Yₛ) = F*0.25/(2A*2Y_c) = 0.25F/(4AY_c) = F/(16AY_c). delta_c = F*L_c/(A_c*Y_c) = F*0.5/(A*Y_c) = 0.5F/(AY_c). delta_c/deltaₛ = (0.5)/(1/16) = 8. So copper extension is 8x steel (Statement A: copper is more - CORRECT). Ratio is 8:1 not 2:1 (Statement B: INCORRECT). Stress on copper = F/A, stress on steel = F/(2A); copper stress is higher (Statement C: CORRECT). Steel does extend (Statement D: INCORRECT). B and D are incorrect.
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