NEET Physics Notes Mechanics-Properties of Matter-Hooke’s Law
Hooke’s Law
Hooke’s Law
According to the Hooke’s law, for any body, within the elastic limit, stress developed is directly proportional to the strain produced.
The ratio of stress to strain, within the elastic limit, is called the coefficient (or modulus) of elasticity for the given material. Depending on the type of stress applied and resulting strain, we have the following three of
Young’s Modulus
Young’s modulus of elasticity (Y) is defined as the ratio of normal stress (either tensile or compressive stress) to the longitudinal strain within a elastic limit.
Bulk Modulus
It is defined as the ratio of the normal stress to the volumetric strain.
Coefficient of volume elasticity.
where, P = \(\frac{F}{A}\) = the pressure or stress negative sign
signifies that for an increase in pressure, the volume will decrease.
Reciprocal of bulk modulus is called compressibility.
Modulus of Rigidity (Shear modulus)
It is defined as the ratio of tangential stress to shearing stress.
Poisson’s Ratio
For a long bar, the Poisson’s ratio is defined as the ratio of lateral strain to longitudinal strain.
Poisson’s ratio is a unitless and dimensionless term. Its value depends on the nature of the material. Theoretically, value of σ must lie between -1 and + 0.5 but for most metallic solids 0 < σ < 0.5
Work Done (or Potential Energy) in a Stretched Wire
Work is done against the internal restoring forces, while stretching a wire. This work is stored as elastic potential energy. The work done is given by
Inter-relations between Elastic Constants
Volume elasticity of a gas .under an isothermal condition is equal to the pressure exerted by the gas 
Adiabatic elasticity of a gas 
, where, y is the ratio of the two principal specific heats of the gas.
Thermal Stress and Strain
When a body is allowed to expand or contract with increasing temperature or decreasing temperature, no stresses are induced in the body. But if the deformation of the body is prevented, some stresses are induced in the body. Such stresses are called thermal stresses or temperature stresses. The corresponding strains are called thermal strains or temperature strains.
A body having linear dimensions is shown in above figure. Let the temperature of the rod is increased by an amount t. The length of the rod would increase by an amount A1, if it were not fixed at two supports. Here,
\(\Delta l=I \alpha t\)
But since the rod is fixed at the supports a compressive strain will be produced in the rod. Because at the increased temperature, the natural length of the rod is \(I+\Delta I\)– while being fixed at two supports its actual length is 1. Hence, thermal strain
Viscosity
Viscosity is the property of a fluid due to which it opposes the relative motion between its different layers.
Here, the constant t| is called the coefficient of viscosity of the given fluid. SI unit of coefficient of viscosity is