Question

Same tension is applied to four wires made of the same material. The elongation is maximum in which wire?

• A. Wire of length 50 cm and diameter 0.5 mm
• B. Wire of length 200 cm and diameter 2 mm
• C. Wire of length 300 cm and diameter 3 mm
• D. Wire of length 100 cm and diameter 1 mm

Hint:

For same material and tension, elongation is proportional to \( \frac{L}{d^2} \).

Answer 1

The Correct Option is A

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.