Simple Stress and Strain MCQ with answer and solution

Concept

E, G and K are related through Poisson's ratio μ: E = 2G(1 + μ) and E = 3K(1 − 2μ).

Formula

E = 2G(1 + μ); E = 3K(1 − 2μ)

Step-by-step solution

1. Given μ = 0.35. 2. Use E = 2G(1 + μ). 3. E = 2G(1 + 0.35) = 2G × 1.35 = 2.7G. 4. Check K: E = 3K(1 − 2 × 0.35) = 3K × 0.3 = 0.9K, so K = E/0.9 ≈ 1.11E. 5. So E = 2.7G is correct. The answer is (C).

Explanation

Young's modulus E and shear modulus G are linked by E = 2G(1 + μ). With μ = 0.35, this gives E = 2.7G. The other relations do not match this value of μ.

Why the other options are wrong

A: E = 1.3G is wrong. It uses (1 + μ) without the factor 2. B: K = 0.9E is wrong. The correct form is E = 0.9K, so K ≈ 1.11E. D: G = 2.7E is reversed. G is always smaller than E.

Shortcut

E/G = 2(1 + μ) = 2 × 1.35 = 2.7.

Common mistake

Forgetting the factor 2 in E = 2G(1 + μ), or mixing up which constant is on which side, as in options B and D.