Modulus of Elasticity

Types of Modulus of Elasticity
1. Young’s Modulus of Elasticity
It is defined as the ratio of normal stress to the longitudinal strain Within the elastic limit.
y = Normal stress / Longitudinal strain
y = FΔl / Al = Mg Δl / πr l
Its unit is N/m or Pascal and its dimensional formula is [ML T ].
2. Bulk Modulus of Elasticity
It is defined as the ratio of normal stress to the volumetric strain within the elastic limit.
K = Normal stress / Volumetric strain
K = FV / A ΔV = &DElta;p V / Δ V
where, Δp = F / A = Change in pressure.
Its unit is N/m or Pascal and its dimensional formula is [ML T ].
3. Modulus of Rigidity (η)
It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit.
η = Tangential stress / Shearing strain
Its urut is N/m or Pascal and its dimensional formula is [ML T ].
Compressibility
Compressibility of a material is the reciprocal of its bulk modulus of elasticity.
Compressibility (C) = 1 / k
Its SI unit is N m and CGS unit is dyne cm .
Steel is more elastic than rubber. Solids are more elastic and gases are least elastic.
For liquids. modulus of rigidity is zero.
Young’s modulus (Y) and modulus of rigidity (η) are possessed by solid materials only.