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 $50cm$ , diameter $0.5mm$
• B. Length $100cm$ , diameter $1mm$
• C. Length $200cm$ , diameter $2mm$
• D. Length $300cm$ , diameter $3mm$

Answer 1

Answer: (A)

$Y=\frac{F / A}{\Delta \ell / \ell }\Rightarrow \Delta \ell =\frac{F L}{A Y}$
$\Delta \ell \propto \frac{L}{D^{2}}$
$\therefore \Delta \ell _{1}:\Delta \ell _{2}:\Delta \ell _{3}:\Delta \ell _{4}$
$=\frac{50}{0 . 5^{2}}:\frac{100}{1^{2}}:\frac{200}{2^{2}}:\frac{300}{3^{2}}=\frac{1}{1}:\frac{2}{4}:\frac{4}{16}:\frac{6}{36}$
$=1:\frac{1}{2}:\frac{1}{4}:\frac{1}{6}$