Question

A composite wire of a uniform cross-section $5.5\times {10}^{-5}{m}^2$ consists of a steel wire of length $1.5m$ and a copper wire of length with a mass of $200kg$ is [Young's modulus of steel is $2\times {10}^{11}N{m}^{-2}$ and that of copper is $1\times {10}^{11}N{m}^{-2}$. Take $g=10m{s}^{-2}]$

• A. $1mm$
• B. $2mm$
• C. $3mm$
• D. $4mm$

Answer 1

The correct option is A $1mm$

$\Delta Ps=F\cdot \frac{P}{A}\cdot Ys$

$=2000\times \frac{1.5}{5.5\times {10}^{-5}}\times 2\times {10}^{11}$

$=\frac{3\times {10}^{-2}}{55\times 2}$

$=0.00027m$

$\Delta Pc=2000\times \frac{20}{5.5\times {10}^{-5}}\times 10\times {10}^{11}$

$=0.00072m$

$\Delta P=\Delta Ps+\Delta Pc=1mm$