The ratio of modulus of rigidity to modulus of elasticity for a Poisson's ratio of 0.25 would be:

(a) 0.5
(b) 0.4
(c) 0.3
(d) 1.0

To calculate the ratio of the modulus of rigidity (GG) to the modulus of elasticity (EE) for a given Poisson's ratio (ν\nu), we can use the following relationship derived from the theory of elasticity:
G=E2(1+ν)G = \frac{E}{2(1 + \nu)}
Where:
• GG is the modulus of rigidity (also known as the shear modulus),
• EE is the modulus of elasticity (also known as Young’s modulus),
• ν\nu is the Poisson’s ratio.
Step 1: Use the formula to express the ratio of GG to EE:
GE=12(1+ν)\frac{G}{E} = \frac{1}{2(1 + \nu)}
Step 2: Substitute the given value of Poisson's ratio ν=0.25\nu = 0.25 into the formula:
GE=12(1+0.25)=12(1.25)=12.5=0.4\frac{G}{E} = \frac{1}{2(1 + 0.25)} = \frac{1}{2(1.25)} = \frac{1}{2.5} = 0.4
Conclusion:
The ratio of the modulus of rigidity (GG) to the modulus of elasticity (EE) for a Poisson's ratio of 0.25 is 0.4.
Therefore, the correct answer is: B. 0.4.