A 100 m long wire having cross-sectional area $$6.25 \times 10^{-4} \text{ m}^2$$ and Young's modulus is $$10^{10} \text{ N m}^{-2}$$ is subjected to a load of 250 N, then the elongation in the wire will be :

We need to find the elongation of a wire subjected to a load, given its dimensions and Young's modulus. Young's modulus is defined as: $$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$$ Rearranging for elongation $$\Delta L$$: $$\Delta L = \frac{FL}{AY}$$

Substituting the given values $$F = 250$$ N, $$L = 100$$ m, $$A = 6.25 \times 10^{-4}$$ m$$^2$$, $$Y = 10^{10}$$ N/m$$^2$$:

$$\Delta L = \frac{250 \times 100}{6.25 \times 10^{-4} \times 10^{10}}$$

$$= \frac{25000}{6.25 \times 10^{6}}$$

$$= \frac{25000}{6250000} = 4 \times 10^{-3} \text{ m}$$

The correct answer is Option (4): $$4 \times 10^{-3}$$ m.