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, $\frac{\Delta\ell_{1}}{\Delta\ell_{2}}=\left(\frac{\ell_{1}}{\ell_{2}}\right)\left(\frac{r_{2}}{r_{1}}\right)^{2}$
$\frac{\Delta\ell_{1}}{\Delta\ell_{2}}=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)^{2}$
$\frac{\Delta\ell_{1}}{\Delta\ell_{2}}=\frac{1}{8}$