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A 100 N load hangs from two wires fixed to a ceiling: a copper wire and a steel wire, each of cross-section 0.5 cm², of lengths sqrt(3) m and 1 m respectively. The copper wire makes 30 deg with the ceiling and the steel wire makes 60 deg with the ceiling. If the copper wire stretches by (deltaₗ_c) and the steel wire by (deltaₗₛ), find the ratio (deltaₗ_c)/(deltaₗₛ). [Young's modulus: copper = 1*10¹¹ N/m², steel = 2*10¹¹ N/m²]
- 1.0
- 2.0
- 0.5
- sqrt(3)
Correct answer: 2.0
Solution
Force balance gives the two tensions, then the elongation formula deltaₗ = T*L/(A*Y) yields the ratio. The numbers conspire so the ratio is exactly 2.
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