Young's moduli of the material of wires $$A$$ and $$B$$ are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]

Elongation: $$\Delta l = \frac{Fl}{AY}$$. For same F and l:

$$\frac{\Delta l_A}{\Delta l_B} = \frac{A_B Y_B}{A_A Y_A} = \frac{3 \times 4}{1 \times 1} = 12$$

The correct answer is Option 1: 12:1.

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