Question

Two wires of same material having radius in ratio $2:1$ and lengths in ratio $1:2$. If same force is applied on them, then ratio of their change in length will be:

• A. 1 : 1
• B. 1 : 2
• C. 1 : 4
• D. 1 : 8

Answer 1

Answer: (D)

Given,
$\frac{r_1}{r_2}=\frac{2}{1}$ and $\frac{{\ell }_1}{{\ell }_2}=\frac{1}{2}$
Young's modulus, $Y=\frac{F}{A}.\frac{\ell }{\Delta \ell }$
So, $\frac{\Delta {\ell }_1}{\Delta {\ell }_2}=\left(\frac{{\ell }_1}{{\ell }_2}\right){\left(\frac{r_2}{r_1}\right)}^2$
$\frac{\Delta {\ell }_1}{\Delta {\ell }_2}=\left(\frac{1}{2}\right){\left(\frac{1}{2}\right)}^2$
$\frac{\Delta {\ell }_1}{\Delta {\ell }_2}=\frac{1}{8}$