Hello students we know that when external force is given to the substance, it undergoes deformation. The quantities stress and strain can be studied in the deformation of substance. It was noticed that the applied force and changes in the dimension are found in proportional and linear till the certain value of force termed as elastic stress. Beyond that particular value of applied force, and the changes produced due to that are become non-linear. The point up to which substance retains the property of elasticity in known elastic limit. Sir, Robert Hooke performed some experiments to study elasticity in details and predicted the important results which are applicable up to elastic region only.
Let’s state the law….!
Statement: – “Within the elastic limit, stress is directly proportional to strain.”
∴ stress α strain
∴ stress = M × strain
Where ‘M’ is constant of proportionality
∴ stress/strain = constant (M)
The constant of proportionality is called as Modulus of elasticity.
Modulus of elasticity ,M = stress/strain
SI unit of Modulus of elasticity is Or N/m2 Or Pascal.
Let’s go in more detail….
As we know that, there are three types of strain and three types of strain; hence the modulus of elasticity is also of three types,
There are three types of module of elasticity:
1) Young’s modulus
2) Bulk modulus
3) Modulus of rigidity
1) Young’s modulus:
The modulus of elasticity related to change in length is known as Young’s modulus.
Young’s modulus is defined as the ratio of tensile stress to the tensile strain
∴ Young^’ s Modulus= (tensile stress)/(tensile strain)
2) Bulk modulus:
The modulus of elasticity related to a change in the volume is bulk modulus (k).
Bulk modulus is defined as the ratio of the volume stress to the volume strain.
∴ Bulk Modulus = Volume Stress/ Volume Strain
3) Modulus of rigidity:
The modulus of rigidity (n) is the modulus of elasticity related to a change in the shape of a body.
The ratio of the sharing stress to the shearing strain is called Modulus of Rigidity.
∴ Modulus of rigidity = shearing stress / shearing strain
Some important points to note……!
- Hooke’s law is valid up to only elastic limit.
- The graph of stress verses strain is straight line up to elastic limit.
- Modulus of elasticity has same unit that of stress.