Correct Answer - Option 1 : 50
Concept:
Bulk Modulus
It is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material.
Mathematically, it is represented as follows:
\(K = \frac{{\Delta P}}{{ - \frac{{\Delta V}}{V}}}\)
where, K: Bulk modulus, ΔP: change of the pressure or force applied per unit area on the material, ΔV: change of the volume of the material due to the compression, V: Initial volume of the material
Relationship between Elastic modulus (E), Bulk modulus (K) and Poisson's ratio (μ):
\(E = 3K\left( {1 - 2μ } \right)\)
Calculation:
Given:
E = 90 GPa, μ = 0.2
\(E = 3K\left( {1 - 2μ } \right)\)
\(K = \frac{E}{{3\left( {1 - 2μ } \right)}} = \frac{{90}}{{3 \times \left( {1 - 2 \times 0.2} \right)}} = 50~GPa\)
Bulk Modulus = 50 GPa
