A steel wire and a copper wire of equal length and equal cross-se… - Vidyadip

Question

A steel wire and a copper wire of equal length and equal cross$-$sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of :

The stresses developed in the two wires,
The strains developed in two wires. Given that $Y$ of steel $= 2.0 \times 10^{11}N/ m^2$ and $Y$ of copper $= 1.1 \times 10^{11}N/ m^2$.

✓

Answer

Here $L_1 = L_2, A_1 = A_2$ and $F$ is same.

Stress $\sigma=\frac{\text{F}}{\text{A}}$ and $F$ and $A$ are common, hence stress in steel wire and in copper wire are equal.
Strain $\varepsilon=\frac{\Delta\text{L}}{\text{L}}=\frac{\text{Stress}}{\text{Y}}$ and stress is equal,

$\therefore\frac{\varepsilon_\text{steel}}{\varepsilon_\text{copper}}=\frac{\text{Y}_\text{ copper}}{\text{Y}_\text{steel}}=\frac{1.1\times10^{11}}{2.0\times10^{11}}=\frac{11}{20}=0.55:1.$

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