Given that for an elastic material poisson's ratio (μ) is 0.4

Explanation:

Poisson's ratio (ν):
Poisson's ratio is a measure of the ratio of lateral strain to longitudinal strain for a material under stress. It is denoted by the Greek letter ν (nu). Poisson's ratio is dimensionless and ranges between -1 and 0.5.

Modulus of Rigidity (G):
Modulus of rigidity, also known as shear modulus, is a measure of the material's resistance to deformation in shear. It represents the ratio of shear stress to shear strain within the elastic limit. It is denoted by the letter G.

Young's Modulus (E):
Young's modulus, also known as modulus of elasticity, is a measure of the stiffness of a material. It represents the ratio of stress to strain within the elastic limit. It is denoted by the letter E.

Ratio of Modulus of Rigidity to Young's Modulus:
The ratio of modulus of rigidity (G) to Young's modulus (E) is given by the formula:

G/E = (1 + ν)/(2(1 - ν))

where ν is the Poisson's ratio.

Given Information:
Poisson's ratio (ν) = 0.4

Calculation:
Using the given value of Poisson's ratio (ν = 0.4), we can calculate the ratio of modulus of rigidity (G) to Young's modulus (E).

G/E = (1 + 0.4)/(2(1 - 0.4))
= 1.4/(2(0.6))
= 1.4/1.2
= 1.1667 (rounded to four decimal places)

Therefore, the ratio of modulus of rigidity (G) to Young's modulus (E) is approximately 1.167.

To round off the answer to three decimal places, we consider the third decimal place. If the value is 5 or greater, we round up the second decimal place. If the value is less than 5, we keep the second decimal place as it is.

In this case, the third decimal place is 7, which is greater than 5. Therefore, the second decimal place (6) is rounded up to 7.

Hence, the final answer is 1.167 rounded off to three decimal places, which is approximately 1.167.

Answer:
The ratio of modulus of rigidity to Young's modulus is 0.357.