Physics - Elasticity Question with Solution | TestHub

Let ${\ell }_0$ be the unstretched length and ${\ell }_3$ be the length under a tension of $9\mathrm{N}$. Then $$\begin{array}{rl}\mathrm{Y}& =\frac{4{\ell }_0}{\mathrm{A}\left({\ell }_1-{\ell }_0\right)}=\frac{5{\ell }_0}{\mathrm{A}\left({\ell }_2-{\ell }_0\right)}\\ & =\frac{9{\ell }_0}{\mathrm{A}\left({\ell }_3-{\ell }_0\right)}\end{array}$$ These give $$\frac{4}{{\ell }_1-{\ell }_0}=\frac{5}{{\ell }_2-{\ell }_0}\Rightarrow {\ell }_0=5{\ell }_1-4{\ell }_2$$ Further, $\frac{4}{{\ell }_1-{\ell }_0}=\frac{9}{{\ell }_2-{\ell }_0}$ Substituting the value of ${\ell }_0$ and solving, we get ${\ell }_3=5{\ell }_2-4{\ell }_1$