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Based on the formula for Young's modulus, Y = F / πr² × L / l, which of the following relationships is accurate?

1. l is directly proportional to L and inversely proportional to r².
2. The ratio of elongations l1 and l2 is given by r2² × L1 / r1² × L2.
3. The elongation ratio l1 : l2 is 1 : 8.
4. Given that Y and F are identical for two wires, elongation l is proportional to L / r².

Correct answer: Given that Y and F are identical for two wires, elongation l is proportional to L / r².

Solution

Young's modulus (Y) is given by Y = (F × L) / (A × l), where A is the cross-sectional area (πr²). Rearranging, we get l ∝ L / r² when Y and F are constant. This matches option D.

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