Question

If Poisson's ratio of a rock sample is \(0.25\), then the relationship among the modulus of elasticity \((E)\), modulus of rigidity \((G)\), and bulk modulus \((K)\) is

• A. \(E=K=G\)
• B. \(E>K>G\)
• C. \(E>G>K\)
• D. \(E=G>K\)

Hint:

Elastic constants are related by \[ \boxed{ E=2G(1+\mu),\qquad E=3K(1-2\mu). } \]

Answer 1

The Correct Option is B

Step 1: Use the elastic constants relations. For an isotropic material, \[ E=2G(1+\mu), \] and \[ E=3K(1-2\mu), \] where \(\mu\) is Poisson's ratio.

Step 2: Substitute \(\mu=0.25\). For the shear modulus, \[ G=\frac{E}{2(1+0.25)} =\frac{E}{2.5} =0.4E. \] For the bulk modulus, \[ K=\frac{E}{3(1-2\times0.25)} =\frac{E}{1.5} =\frac{2E}{3} \approx0.667E. \] Therefore, \[ E>K>G. \] Hence, \[ \boxed{(B)} \] is the correct answer.