Explanation

(c) Increase in length$l = \frac{FL}{AY}$
or $l = \frac{FL}{\pi\ r^{2}Y}$
Percent increase in length
$\mathrm{\Delta}x = \frac{l}{L} \times 100 = \frac{F}{\pi r^{2}Y}$
Here, same longitudinal force is applied.
So, $\frac{\mathrm{\Delta}x_{1}}{\mathrm{\Delta}x_{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} \bullet \left( \frac{Y_{2}}{Y_{1}} \right)$
$\frac{1}{\mathrm{\Delta}x_{2}} = \left( \frac{1}{2} \right)^{2} \bullet \left( \frac{2}{1} \right) = \frac{1}{4} \times \frac{2}{1}$
$\frac{1}{\mathrm{\Delta}x_{2}} = \frac{1}{2}$
$\mathrm{\Delta}x_{2} = 1 \times 2 = 2\%$