Physics - Elasticity Question with Solution | TestHub

For same material the ratio of stress to strain is same For first cube $${\text{ Stress }}_1=\frac{{\text{ force }}_1}{{\text{ area }}_1}=\frac{10^5}{\left(0.1^2\right)}$$ For second block, $$\begin{array}{rl}& {\text{ stress }}_2=\frac{{\text{ force }}_2}{{\text{ area }}_2}=\frac{10^5}{\left(0.2^2\right)}\\ & {\text{ strain }}_2=\frac{\text{ change in length }{}_2}{\text{ original length }}=\frac{x}{0.2}\end{array}$$ $x$ is the displacement for second block. For same material, $\frac{{\text{ stress }}_1}{{\text{ strain }}_1}=\frac{{\text{ stress }}_2}{{\text{ strain }}_2}$ $$\text{ or, }\frac{\frac{10.5}{(0.1{)}^2}}{\frac{0.5\times 10^{-2}}{0.1}}=\frac{\frac{10^5}{(0.2{)}^2}}{\frac{x}{0.2}}$$ $$\text{ Solving we get, }x=0.25\mathrm{cm}$$