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 steel and copper wire
$Y$ of steel is $2\times {10}^{11}{\text{N/m}}^2$ and $Y$ of copper is $1.3\times {10}^{11}{\text{N/m}}^2$.

Answer 1

Tension is same in both steel and copper,
$F_{st}=F_{cu}$
Area of steel = $A_{st}$
Area of copper = $A_{cu}$
${\text{Stress}}_{st}=\frac{F_{st}}{A_{st}}$.....(1)
${\text{Stress}}_{cu}=\frac{F_{cu}}{A_{cu}}$....(2)
Divide (1) by (2) we get
$\frac{{\text{Stress}}_{st}}{{\text{Stress}}_{cu}}$ = 1