Two wires made of same material are subjected to forces in the ratio 1:4 their lengths are in the ratio 2:1 and diameters in the ratio 1:3, what is the ratio of their extensions?

Explanation

To find the ratio of extensions of two wires made of the same material, we can use the formula derived from the relationship between stress, strain, and Young's modulus. The formula for extension (ΔL) in terms of force (F), length (L), and cross-sectional area (A) is given by:

\[ \frac{F_1}{A_1 \cdot L_1} \cdot \frac{\Delta L_1}{L_1} = \frac{F_2}{A_2 \cdot L_2} \cdot \frac{\Delta L_2}{L_2} \]

### Step-by-step Solution:

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