Question

A material has a young’s modulus of 1.25 × 10⁵ N/mm² and a Poisson’s ratio of 0.25. The bulk modulus of the material will be

1. 83 × 10⁵ N/mm²
2. 0.83 × 10⁵ N/mm²
3. 8.3 × 10³ N/mm²
4. 8.3 × 10⁵ N/mm²

Answer 1

Correct Answer - Option 2 : 0.83 × 10⁵ N/mm²

Concept:

The relation between E, G, μ, and k will be,

E = 2G (1 + μ),

E = 3K (1 – 2μ)

Where E = Young’s modulus, G = Modulus of rigidity, μ = Poisson ratio, K = Bulk modulus of elasticity.

Calculation:

Given:

E = 1.25 × 105 N/mm2, μ = 0.25 

E = 3K (1 – 2μ)

\({\rm{K}} = \frac{{\rm{E}}}{{3\left( {1 - 2{\rm{\mu }}} \right)}} = \frac{{1.25\times 10^5}}{{3\left( {1 - 2 \times 0.25} \right)}} = 0.83\times 10^5\;{{N}}/{{{mm}}^2}\)

The bulk modulus will be 0.83 × 105 N/mm2.