Q.A steel rod of length $1.5\ \text{m}$ and cross-sectional area $2.5\times10^{-4}\ \text{m}^2$ is stretched by a tensile force of $75{,}000\ \text{N}$ applied along its length. Taking the Young's modulus of steel as $Y = 2.0\times10^{11}\ \text{Pa}$, find

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.

Young's modulus can be measured experimentally by suspending a long, thin, uniform wire vertically from a rigid support, measuring its original length and (using a screw gauge) its radius, then hanging a series of known loads from its free end and measuring the resulting elongation for each load (using a vernier arrangement or a reference marker and micrometer, to keep the measurement precise for the very small elongations involved). Plotting load against elongation gives a straight line within the elastic limit, whose slope, combined with the wire's original length and cross-sectional area, gives $Y = MgL/\pi r^2 l$ directly from the measured quantities.

Young's modulus is drawn straight from the NCERT Class 11 Physics chapter on Mechanical Properties of Solids, and its experimental-determination questions are a CBSE board-exam and JEE Main favourite. This is exactly the kind of concept behind searches for "Young's modulus formula and SI unit" or "Young's modulus experiment class 11 physics".