Question

In an experiment it is found that the bulk modulus (K) of a material is equal to its shear modulus (G). The Poisson's ratio is
1. 0.125
2. 0.25
3. 0.375
4. 0.5 

Answer 1

Correct Answer - Option 1 : 0.125

Concept:

As we know that the relationship between modulus of elasticity E, shear modulus G, bulk modulus K and Poisson’s ratio μ

E = 3K(1-2μ)

E = 2G(1+μ)

\(E = \frac{{9KG}}{{3K + G}}\)

\(μ = \frac{{3K - 2G}}{{6K + 2G}}\)

Calculation:

Given:

K= G

\(μ = \frac{{3K - 2G}}{{6K + 2G}}\)

\(μ = \frac{{3 - 2}}{{6+ 2}}\)

\(μ = \frac{{1}}{{8}}\)

μ = 0.125