Physics - Elasticity Question with Solution | TestHub

Tension is rod at a distance x from lower end is $\frac{\mathrm{mxg}}{\ell }$ Y is young modulus of elasticity then change in length in dx element is dy

$$\begin{array}{rlrlrlrl}& Y\times \text{ strain }=\text{ stress }& Y\times \frac{dy}{dx}=\frac{T}{A}& Y\times \frac{dy}{dx}=\frac{mgx}{\ell \times A}& {\int }_0^{T}Ydy={\int }_0^T\frac{mg}{\ell A}\times xdx& Yy=\frac{mg}{\ell A}\left[\frac{(70{)}^2-(30{)}^2}{2}\right]& y=\frac{mg}{AY\times 100}\times 2000& y=\frac{mg}{AY}\times 20\end{array}$$

Total length is $=40\mathrm{cm}=20\frac{\mathrm{mg}}{\mathrm{AY}}\mathrm{cm}$