Use this formula - young modulus = 2× rigidity ×
( 1+ poisons ratio) . ans will come 0.2

Young's Modulus and Modulus of Rigidity

Young's modulus (E) and modulus of rigidity (G) are two fundamental mechanical properties used to describe the behavior of materials under deformation.

Young's modulus quantifies the stiffness of a material and measures its resistance to elastic deformation when subjected to an external force. It is defined as the ratio of stress to strain within the elastic limit. Young's modulus is given by the equation:

E = stress/strain

Modulus of rigidity, also known as shear modulus, measures a material's resistance to shear deformation when an external force is applied parallel to its surface. It is defined as the ratio of shear stress to shear strain. Modulus of rigidity is given by the equation:

G = shear stress/shear strain

Relationship between Young's Modulus and Modulus of Rigidity

The given relationship states that Young's modulus is 2.4 times the modulus of rigidity (E = 2.4G). Let's analyze this relationship to determine its implications.

Calculating Poisson's Ratio

Poisson's ratio (ν) is a dimensionless quantity that relates the lateral strain (strain perpendicular to the applied force) to the axial strain (strain parallel to the applied force) in a material. It is defined as the negative ratio of the lateral strain to the axial strain:

ν = -lateral strain/axial strain

Using the relationship between Young's modulus and modulus of rigidity, we can derive an expression for Poisson's ratio.

From the definition of Young's modulus (E = stress/strain), we have:

E = stress/axial strain (1)

From the definition of modulus of rigidity (G = shear stress/shear strain), we have:

G = shear stress/shear strain (2)

Rearranging equations (1) and (2), we get:

stress = E * axial strain (3)

shear stress = G * shear strain (4)

Deriving the Expression for Poisson's Ratio

Consider a material under uniaxial stress in the x-direction. Due to the applied force, the material experiences elongation in the x-direction (axial strain) and contraction in the y and z-directions (lateral strain).

Let's assume a small strain in the y-direction (lateral strain) and calculate its value.

Using Hooke's law, the stress in the y-direction is given by:

stress_y = -ν * stress_x

From equation (3), we have:

stress_x = E * axial strain

Substituting this into the stress_y equation, we get:

stress_y = -ν * E * axial strain

Using equation (4), we can express the shear strain in terms of the lateral strain:

shear strain = lateral strain/2

Therefore, shear stress can be written as:

shear stress = G * (lateral strain/2)

Equating the expressions for shear stress, we have:

G * (lateral strain/2) = -ν * E * axial strain

Rearranging the equation, we find:

lateral strain/axial strain = -2ν * (G/E)

Since Poisson's ratio is defined as the negative ratio of the lateral strain to the axial strain, we have:

ν = -0.5 * (l