Question

The following four wires of the same material, which of these will have the largest extension when the same tension is applied –

• A. Length = 50 cm & diameter = 0.5 mm
• B. Length = 100 cm & diameter = 1 mm
• C. Length = 200 cm & diameter = 2 mm
• D. Length = 300 cm & diameter = 3 mm

Answer 1

Answer: (A)

Length = 50 cm & diameter = 0.5 mm

Answer 2

We know Y = $\frac{F\mathcal{l}}{(\pi r^{2})\Delta\mathcal{l}}$ Ž Dl = $\frac{F\mathcal{l}}{Y(\pi r^{2})}$

F and Y same so Dl µ $\frac{\mathcal{l}}{r^{2}}$

So wire which have l/r² maximum have maximum extension.