Simple Stress and Strain MCQ with answer and solution

Concept

Relationship between elastic constants

Formula

E = 9KG / (3K + G)

Step-by-step solution

1. Elastic constants E (Young's modulus), G (Shear modulus), and K (Bulk modulus) define the elastic behavior of isotropic materials. 2. The relation between E, G, and K is derived using Poisson's ratio μ, where E = 2G(1 + μ) and E = 3K(1 - 2μ). 3. Eliminating Poisson's ratio μ yields the standard relationship E = 9KG / (3K + G). Answer: D

Explanation

The relationship between the elastic constants Modulus of Elasticity (E), Modulus of Rigidity (G), and Bulk Modulus (K) is derived from elasticity equations for isotropic materials. Expressing Poisson's ratio in terms of E, G, and K and setting the expressions equal yields E equals 9KG divided by 3K plus G. Thus, option D gives the correct formula connecting these three elastic constants.

Why the other options are wrong

A) This formula lacks the multiplier 9 in the numerator and 3 before K in the denominator. B) The denominator is missing the factor of 3 for K in the relation E = 9KG / (3K + G). C) The factor 3 should multiply K in the denominator rather than G.

Shortcut

Elastic constants relationship: E = 9KG / (3K + G).

Common mistake

Misremembering the exact formula coefficients in the denominator for combining elastic constants E, G, and K.