To calculate the modulus of rigidity, we can use the relationship between the modulus of elasticity (E) and the Poisson's ratio (ν). The modulus of rigidity (G) is related to these parameters by the equation:

G = E / (2 * (1 + ν))

Given that the modulus of elasticity (E) is 200 GN/m^2 and the Poisson's ratio (ν) is 0.25, we can substitute these values into the equation to find the modulus of rigidity (G).

Calculation:

E = 200 GN/m^2
ν = 0.25

G = E / (2 * (1 + ν))
G = 200 GN/m^2 / (2 * (1 + 0.25))
G = 200 GN/m^2 / (2 * 1.25)
G = 200 GN/m^2 / 2.5
G = 80 GN/m^2

Therefore, the modulus of rigidity is 80 GN/m^2.

Explanation:

The modulus of rigidity, also known as the shear modulus or the elastic modulus in shear, measures a material's resistance to deformation in shear or torsion. It is a fundamental property of materials and is commonly used in engineering calculations involving shear stress and strain.

Poisson's ratio is a dimensionless quantity that describes the ratio of lateral strain to axial strain when a material is subjected to uniaxial stress. It is a measure of the material's ability to expand or contract in perpendicular directions when compressed or stretched.

The relationship between the modulus of elasticity (E), the Poisson's ratio (ν), and the modulus of rigidity (G) is derived using the principles of linear elasticity. When a material is subjected to a shear stress, it experiences a shear strain, which is directly proportional to the shear stress. The modulus of rigidity is the constant of proportionality between shear stress and shear strain.

In this case, the given values are E = 200 GN/m^2 and ν = 0.25. By substituting these values into the equation G = E / (2 * (1 + ν)), we find that G = 80 GN/m^2.

Therefore, the correct answer is option A) 80 GN/m^2.