Question

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)

• A. $2.77\times 10^{-2}mm$
• B. $6.9\times 10^{-2}mm$
• C. $6.06\times 10^{-2}mm$
• D. $3.0\times 10^{-2}mm$

Answer 1

Answer: (B)

$Y=\frac{F/A}{\frac{\Delta \ell }{\ell }}$
$\Rightarrow F=\frac{YA}{\ell }\Delta \ell$
${\left(\frac{A\Delta \ell }{\ell }\right)}_1={\left(\frac{A\Delta \ell }{\ell }\right)}_2$
$\Rightarrow \frac{\Delta {\ell }_2}{\Delta {\ell }_1}=\frac{A_1}{A_2}\times \frac{{\ell }_2}{{\ell }_1}$
$\Rightarrow \frac{\Delta {\ell }_2}{0.2}=\frac{1}{2.4\times 2.4}\times \frac{2}{1}$
$\Rightarrow \Delta {\ell }_2=6.9\times 10^{-2}mm$