Young’s moduli of the material of wires A and B are in the...

The formula to calculate the elongation of a metallic wire because of the application of a load can be written as

$$\begin{array}{ll}\DeltaL = \left(\dfrac{FL}{AY}\right)\end{array}$$. . . \left(1\right)$</p><p>The ratio of the elongations for both the wires is, then, calculated as follows-</p><p>$\begin{cases}\dfrac{∆ {L}_{1}}{∆ {L}_{2}} & = & \dfrac{\dfrac{FL}{{A}_{1}{Y}_{1}}}{\dfrac{FL}{{A}_{2}{Y}_{2}}} \\ & = & \dfrac{{A}_{2}{Y}_{2}}{{A}_{1}{Y}_{1}} \\ & = & \dfrac{3}{1} \times \dfrac{4}{1} \\ & = & \dfrac{12}{1}\end{cases}$