What is Young’s modulus ? Explain. and Give its unit and dimensional formula.

Experimental observation show that for a given material the magnitude of the strain produced is same whether the stress is tensile or compressive.

The ratio of tensile (or compressive) stress $(\sigma)$ to the longitudinal strain $(\varepsilon)$ is defined as Young's modulus and is denoted by the symbol Y.

$\text { Young modulus }=\frac{\text { Tensile stress }(\sigma)}{\text { Longitudinal } \operatorname{strain}(\varepsilon)}$

$\quad \mathrm{Y}=\frac{\sigma}{\varepsilon}$

$\therefore \mathrm{Y}=\frac{(\mathrm{F} / \mathrm{A})}{(\Delta \mathrm{L} / \mathrm{L})}=\frac{(\mathrm{F} \times \mathrm{L})}{(\mathrm{A} \times \Delta \mathrm{L})}$

Here, strain is a dimensionless quantity, the unit of Young's modulus is the same as that of stress. Mean $\mathrm{N} \mathrm{m}^{-2}$ or Pascal $(\mathrm{P} a)$.

Dimensional formula : $\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$.

Young's moduli, elastic limit and tensile strength of some materials are given below.

Substance	Young's Modulus $10^{9} \mathrm{~N} / \mathrm{m}^{2}$ $\sigma_{y}$	Elastic limit $10^{7} \mathrm{~N} / \mathrm{m}^{2}$ $%$	Tensile  strength $10^{7} \mathrm{~N} / \mathrm{m}^{2}$ $\sigma_{u}$
Aluminium	$70$	$18$	$20$
Copper	$120$	$20$	$40$
Iron (Wrought)	$190$	$17$	$33$
Steel	$200$	$30$	$50$
Bone (Tensile) (Compressive)	$16$ $9$		$12$ $12$

For metals Young's moduli are large therefore these materials require a large force produce small change in length.

Steel is more elastic than copper, brass and aluminium. It is for this reason that steel is preferred in heavy-duty machines and in structural designs.

Wood, bone, concrete and glass have rather small Young's moduli.