JEE Main 2024 — 29 January, Shift 2 — Question 42

$Y=\frac{\text { stress }}{\text { strain }}$

$\mathrm{Y}=\frac{\frac{\mathrm{F}}{\pi \mathrm{r}^{2}}}{\frac{\ell}{\mathrm{~L}}}$ $\mathrm{F}=\mathrm{Y} \pi \mathrm{r}^{2} \times \frac{\ell}{\mathrm{L}}$ $\mathrm{Y}=\frac{\frac{\mathrm{F} / 2}{\pi \mathrm{r}^{2} / 4}}{\frac{\Delta \ell}{\mathrm{~L}}}$ $\mathrm{F}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} \times 2 \times \frac{\pi \mathrm{r}^{2}}{4}$ From (i) $\mathrm{Y} \pi \mathrm{r}^{2} \frac{\ell}{\mathrm{~L}}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} \frac{\pi \mathrm{r}^{2}}{2}$ $\Delta \ell=2 \ell$