The Young's modulus of the material of a wire is 6 x 10^12 N/m2 and there is no transverse strain. The modulus of rigidity is
To find the modulus of rigidity, we first need to understand its definition. Modulus of rigidity, also known as shear modulus, is a measure of a material's ability to resist deformation when a force is applied parallel to one face of the material while the opposite face is held fixed.
We are given that the Young's modulus (denoted as E) of the material is 6 x 10^12 N/m^2 and there is no transverse strain. The relationship between Young's modulus (E) and modulus of rigidity (G) is given by the following equation:
E = 2G(1 + ν)
where ν is the Poisson's ratio, which represents the ratio of transverse strain to the corresponding axial strain.
Since there is no transverse strain (ν = 0), we can simplify the equation as follows:
E = 2G(1 + 0)
E = 2G
Now, we can solve for G by rearranging the equation:
G = E/2
Substituting the given value of Young's modulus, we have:
G = (6 x 10^12 N/m^2) / 2
Simplifying the expression yields:
G = 3 x 10^12 N/m^2
Therefore, the modulus of rigidity (or shear modulus) of the material is 3 x 10^12 N/m^2.