Question

A copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ 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 $1\, mm$. If the Young’s modulii of copper and steel are respectively $1.0 \times10^{11}\,Nm^{-2}$ and $2.0 \times 10^{11}\,Nm^{-2},$ the total extension of the composite wire is :

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

Answer 1

Answer: (D)

$Y_{c}\times\left(\Delta L_{c}/L_{c}\right)=Y_{s}\times\left(\Delta L_{s}/L_{s}\right)$
$\Rightarrow 1\times10^{11}\times\left(\frac{1\times10^{-3}}{1}\right)=2\times10^{11}\times\left(\frac{\Delta L_{5}}{0.5}\right)$
$\therefore \Delta L_{s}=\frac{0.5\times10^{-3}}{2}=0.25\,mm$
Therefore, total extension of the composite
wire $= \Delta L_{c}+\Delta L_{s}$
$= 1\,mm+0.25\,m= 1.25\,m$