Question:
Same tension is applied to four wires made of the same material. The elongation is maximum in which wire?
Same tension is applied to four wires made of the same material. The elongation is maximum in which wire?
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For same material and tension, elongation is proportional to \( \frac{L}{d^2} \).
Updated On: Mar 18, 2026
- Wire of length 50 cm and diameter 0.5 mm
- Wire of length 200 cm and diameter 2 mm
- Wire of length 300 cm and diameter 3 mm
- Wire of length 100 cm and diameter 1 mm
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The Correct Option is A
Solution and Explanation
Elongation formula: \( \Delta L = \frac{FL}{A Y} \Rightarrow \Delta L \propto \frac{L}{A} = \frac{4L}{\pi d^2} \) for same tension and same material (same \( Y \))
Compute \( \frac{L}{d^2} \) for all options: - (1): \( \frac{50}{0.5^2} = \frac{50}{0.25} = 200 \) ← Maximum
- (2): \( \frac{200}{4} = 50 \)
- (3): \( \frac{300}{9} \approx 33.33 \)
- (4): \( \frac{100}{1} = 100 \) So, option (1) has highest value → maximum elongation.
Compute \( \frac{L}{d^2} \) for all options: - (1): \( \frac{50}{0.5^2} = \frac{50}{0.25} = 200 \) ← Maximum
- (2): \( \frac{200}{4} = 50 \)
- (3): \( \frac{300}{9} \approx 33.33 \)
- (4): \( \frac{100}{1} = 100 \) So, option (1) has highest value → maximum elongation.
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