\( \mathrm{Y}=\frac{\frac{\mathrm{F}}{\mathrm{r}^2}}{\frac{\ell}{\mathrm{L}}} \)

\( \mathrm{F}=\mathrm{Y} \pi \mathrm{r}^2 \times \frac{\ell}{\mathrm{L}} \)  \(...........(i)\)

\( \mathrm{Y}=\frac{\frac{\pi \mathrm{r}^2 / 4}{\Delta \ell}}{\mathrm{L}} \)

\( \mathrm{F}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} \times 2 \times \frac{\pi \mathrm{r}^2}{4} \)

\( \text { From }(\mathrm{i}) \)

\( \mathrm{Y} \pi \mathrm{r}^2 \frac{\ell}{\mathrm{L}}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} \frac{\pi \mathrm{r}^2}{2} \)

\( \Delta \ell=2 \ell\)