Question

The ratio of lengths of two wires made of same material is $2:3$. The ratio of their respective longitudinal stress to produce same elongation is

• A. $4:9$
• B. $9:4$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is D $3:2$

$\frac{L_1}{L_2}=\frac{2}{3}$

$\Delta L_1=\Delta L_2$ (given)

$y_1=y_2$ (given)

$\frac{{\sigma }_1}{{ϵ}_1}=\frac{{\sigma }_2}{{ϵ}_2}$ (as inferred from question)

$\frac{{\sigma }_1}{{\sigma }_2}=\frac{{ϵ}_1}{{ϵ}_2}$

$\frac{{\sigma }_1}{{\sigma }_2}=\frac{\Delta L_1}{L_1}\times \frac{L_2}{\Delta L_2}$$=\frac{3}{2}\times 1$