Revision: Elasticity Physics HSC Science (General) 12th Standard Board Exam Maharashtra State Board

When equal normal forces are applied on every surface of a body causing a change in volume, the restoring force opposing this change per unit area is called hydraulic stress (also called volume stress).

Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.

OR

The ratio of change in configuration to the original configuration is called strain.

• It has no unit and no dimensions (pure ratio).

The ratio of change in length of the body to its initial length is called longitudinal strain: ε = ΔL/L.

The angular displacement of the surface in direct contact with the applied shear stress from its original position is called shear strain: τ = W/L = tan ⁡θ.

When there is an increase in the length or extension of the body in the direction of the applied force, the stress produced is called tensile stress.

When there is a decrease in the length or compression of the body due to the applied force, the stress produced is called compressive stress.

The strain is defined as the ratio of change in dimensions of the body to its original dimensions.

Strain = `"change in dimensions"/"original dimensions"`

The ratio of change in volume of the body to its original volume is called volume strain: ΔV/V.

The internal restoring force per unit area of a body is called stress.

OR

The internal restoring force acting per unit area of a deformed body is called stress.

• SI Unit: N/m² (pascal, Pa)
   Dimensions: [M¹L⁻¹T⁻²]

The modulus of elasticity of a material is the ratio of stress to the corresponding strain. It is defined as the slope of the stress-strain curve in the elastic deforming region and depends on the nature of the material.

\[\frac {stress}{strain}\] = Constant

The constant is called the modulus of elasticity.

OR

The constant ratio of stress to strain within the elastic limit is called the Modulus of Elasticity.

The reciprocal of the bulk modulus is called compressibility: k = \[\frac {1}{B}\].

The point on the stress-strain curve up to which Hooke's Law is valid is called the proportional limit (Point A).

The stress at the yield point (end of elastic behavior and start of plastic deformation) is called the yield strength.

The maximum stress that a material can withstand is called the Ultimate Tensile Strength (Point D).

The point at which the material breaks and failure of the material takes place is called the fracture point (Point E).

Hooke's Law was discovered by English scientist Robert Hooke in 1660. He first stated it as a Latin anagram: "As the extension, so the force."

Statement: For small deformations, stress is directly proportional to strain, within the elastic limit.

Key Points:

• Hooke's Law is a measure of elasticity.
• It is valid only up to the elastic limit. Beyond this, the material does not return to its original shape and Hooke's Law no longer applies.
• In springs: The force needed to extend or compress a spring by distance x is proportional to that distance → F = −kx (where k is the spring constant).
• Hooke's Law is applicable only in the case of elastic deformation.