Derive relationship for
(i) young's modulus
(ii)bulk Modulus
(iii) modulus of rigidity
Answers
Explanation:
(i) Young’s modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. Sometimes referred to as the modulus of elasticity, Young’s modulus is equal to the longitudinal stress divided by the strain.
(ii) Bulk modulus
Measure of how incompressible / resistant to compressibility a substance is
The bulk modulus ({\displaystyle K}K or {\displaystyle B}B) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.
(iii) Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus and bulk modulus. The shear modulus of material gives us the ratio of shear stress to shear strain in a body.
Measured using the SI unit pascal or Pa.
The dimensional formula of Shear modulus is M1L-1T-2.
It is denoted by G.
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