Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is:
$y=\frac{Y_{1} Y_{2}}{Y_{1}+Y_{2}}$
$y=\frac{2 Y_{1} Y_{2}}{3\left(Y_{1}+Y_{2}\right)}$
$Y=\frac{2 Y_{1} Y_{2}}{Y_{1}+Y_{2}}$
${Y}=\frac{{Y}_{1} {Y}_{2}}{2\left({Y}_{1}+{Y}_{2}\right)}$
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Figure shows graph between stress and strain for a uniform wire at two different femperatures. Then
The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is..... $mm$