Q.A telephone wire 125 m long and 1 mm in radius is stretched to a length of 125.25 m when a force of 800 N is applied. What is the value of Young's modulus for the material of the wire?

Young's modulus $Y$, named after the physicist Thomas Young, is the modulus of elasticity associated with a change in length of an object such as a wire, rod or beam — the elasticity of length. It applies to solids only. For a wire of length $L$ and radius $r$, loaded with mass $M$ at its free end and producing an elongation $l$, the longitudinal stress is $Mg/\pi r^2$ and the longitudinal strain is $l/L$, so

Its SI unit is $\text{N/m}^2$ and its dimensional formula is $[L^{-1}M^1T^{-2}]$.

Young's modulus measures how strongly a solid resists being stretched or compressed along its length: a large $Y$ (steel, $21\times10^{10}$ Pa) means the material barely stretches under a given tensile stress, while a small $Y$ (lead, $1.5\times10^{10}$ Pa) means it stretches comparatively much more for the same stress — this makes Young's modulus one of the most practically useful single numbers for characterising a solid material under tension or compression. …