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The change in length ΔL is given by the formula ΔL = FL / πD²Y. Which of the following expressions correctly represents the ratio of elongations for two different cases?

1. ΔLs / ΔLc = Fs / Fc × (Ds / Dc)² × Ys / Yc × Ls / Lc
2. 7 / 5 × (1 / p) × (1 / s) × q
3. The ratio of L / D² is maximum for case (d).
4. According to the formula, ΔL = FL / AY

Correct answer: ΔLs / ΔLc = Fs / Fc × (Ds / Dc)² × Ys / Yc × Ls / Lc

Solution

The given formula ΔL = FL / πD²Y relates the increase in length to force, length, diameter, and Young's modulus. Option A correctly derives the ratio of elongations for two different cases using this formula.

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