A rubber cord L metre long and having A m² area of cross-section is suspended vertically. If the wire extends by $\mathrm{\Delta L}$ under its own weight, then change in length ($\mathrm{\Delta L}$) is: (Take, density of rubber = D kgm^-3 and Young's modulus of rubber = E Nm^-2).  

Volume of the rubber cord = AL

Weight of the rubber cord = ALDg

$\therefore \text{ Stress }=\frac{\mathrm{ALDg}}{\mathrm{A}}=\mathrm{LDg}$

The weight of the rubber cord acts at the centre of gravity which is  $\frac{\mathrm{L}}{2}$from the top.

$\therefore \text{ Strain }=\frac{\mathrm{l}}{\mathrm{L}/2}=\frac{2\mathrm{l}}{\mathrm{L}}$

So,   Youngs modulus,   $\mathrm{E}=\frac{\text{ Stress }}{\text{ Strain }}=\frac{\mathrm{LDg}}{2\mathrm{l}/\mathrm{L}}=\frac{{\mathrm{L}}^2\mathrm{Dg}}{2\mathrm{l}}\text{ or }\mathrm{l}=\frac{{\mathrm{L}}^2\mathrm{Dg}}{2\mathrm{E}}$