An iron rod of length $2 \,m $ and area of cross-section $ 50\,mm^{2}$ stretches by $ 0.5\,mm $ , when a mass of $250\, kg$ is hung from its lower end. The Young's of iron rod is:
When strain is small, the ratio of the longitudinal stress to the corresponding longitudinal strain is called the Young's moduls of the material of the body.
$Y =\frac{\text { longitudinal stress }}{\text { longitudinal strain }} $ $=\frac{F / A}{l / L} $ Given, $=2\, m , $ $A=50 \,mm ^{2} $ $=50 \times 10^{-6} m ^{2} $ $l=0.5 \,mm $ $=0.5 \times 10^{-3}\, m , $ $m=250 \,kg$ $g=9.8\, m / s ^{2}$ $Y=\frac{250 \times 9.8}{50 \times 10^{-6}} \times \frac{2}{0.5 \times 10^{-3}}$ $Y=19.6 \times 10^{10}\, N / m ^{2}$ Note : Young's modulus can be determined only for solids and it is the characteristic of the material of a solid.
Mechanical properties of solids intricate the characteristics such as the resistance to deformation and their strength. Strength is the ability of an object to resist the applied stress, to what extent can it bear the stress.
Therefore, some of the mechanical properties of solids involve:
Elasticity: When an object is stretched, it changes its shape and when we leave, it retrieves its shape. Or we can say it is the property of retrieving the original shape once the external force is removed. For example Spring
Plasticity: When an object changes its shape and never attains its original shape even when an external force is removed. It is the permanent deformation property. For example Plastic materials.
Ductility: When an object is been pulled in thin sheets, wires or plates, it will be assumed that it has ductile properties. It is the property of drawing into thin wires/sheets/plates. For example Gold or Silver
Strength: The ability to hold out applied stress without failure. Many types of objects have higher strength than others.
