Question

For a given material assume, Young’s modulus E = 300 GN/m² and Modulus of rigidity G = 150 GN/m². Its Bulk modulus K will be
1. 120 GN/m²
2. 100 GN/m²
3. 200 GN/m²
4. 250 GN/m²

Answer 1

Correct Answer - Option 2 : 100 GN/m²

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 = 300 GN/m2, G = 150 GN/m2

E = 2G (1 + μ)

300 = 2 × 150 (1 + μ)

μ = 0

E = 3K (1 – 2μ)

\({\rm{K}} = \frac{{\rm{E}}}{{3\left( {1 - 2{\rm{\mu }}} \right)}} = \frac{{300}}{{3\left( {1 - 2 \times 0} \right)}} = 100\;{\bf{GN}}/{{\bf{m}}^2}\)

The bulk modulus will be 100 GN/m2.