Question

Two wires of different materials, each $2m$ long and of diameter $2mm$, are joined in series to form a composite wire. What force will produce a total extension of $0.9mm$ ? ($Y_1=2\times {10}^{11}Pa$ and $Y_2=6\times {10}^{11}Pa$)

• A. $282.6N$
• B. $212N$
• C. $319.8N$
• D. $382.6N$

Answer 1

The correct option is B $212N$

$\begin{array}{c}\text{Given, two wires of length}=2m\\ \text{diameter}=2mm\\ Y_1=2\times {10}^{11}Pa,Y_2=6\times {10}^{11}Pa\\ 0.9\times {10}^{-3}=\text{Total extension.}\end{array}$

$\begin{array}{cc}\Delta l_1+\Delta l_2& =9\times {10}^{-4}\\ \frac{FL}{Y_{1}A}+\frac{FL}{Y_{2}A}& =9\times {10}^{-4}\\ \frac{2F}{\pi \left({10}^{-6}\right)}\times (\frac{1}{2\times {10}^{11}}+\frac{1}{6\times {10}^{11}})& =9\times {10}^{-4}\\ \frac{2F}{\pi \left({10}^{-6}\right)}& \times \frac{4}{6\times {10}^{11}}=9\times {10}^{-4}\\ \Rightarrow & F=212N.\end{array}$