Question

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?

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

Answer 1

Answer: (B)

length = 50 cm, diameter = 0.5 mm

Answer 2

Y = $\frac {F/A}{\Delta \ell/\ell } \Rightarrow \Delta\ell = \frac{F \ell}{YA} = \frac {F \ell}{Y \pi r^2}\Rightarrow \Delta \ell \propto \frac{\ell}{r^2}$ Which is maximum for $\ell = 50 \,\, cm \,\, \&\,\, diameter = 0.5\,\,mm$