Question

A copper wire of length $1.0m$ and a steel wire of length $0.5m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1mm$. If the Young’s modulii of copper and steel are respectively $1.0\times 10^{11}N{m}^{-2}$ and $2.0\times 10^{11}N{m}^{-2},$ the total extension of the composite wire is :

• A. $1.75mm$
• B. $2.0mm$
• C. $1.50mm$
• D. $1.25mm$

Answer 1

Answer: (D)

$Y_c\times \left(\Delta L_c/L_c\right)=Y_s\times \left(\Delta L_s/L_s\right)$
$\Rightarrow 1\times 10^{11}\times \left(\frac{1\times 10^{-3}}{1}\right)=2\times 10^{11}\times \left(\frac{\Delta L_5}{0.5}\right)$
$\therefore \Delta L_s=\frac{0.5\times 10^{-3}}{2}=0.25mm$
Therefore, total extension of the composite
wire $=\Delta L_c+\Delta L_s$
$=1mm+0.25m=1.25m$