Question

The average Young's modulus and Poisson's ratio values of a limestone sample are \(60\ \text{MPa}\) and \(0.3\) respectively. The shear modulus in MPa is

• A. \(17\)
• B. \(20\)
• C. \(23\)
• D. \(26\)

Hint:

The shear modulus is given by \[ \boxed{ G=\frac{E}{2(1+\mu)}. } \]

Answer 1

The Correct Option is C

Step 1: Use the relation between Young's modulus and shear modulus. \[ E=2G(1+\mu). \] Hence, \[ G=\frac{E}{2(1+\mu)}. \]

Step 2: Substitute the given values. Given, \[ E=60\ \text{MPa}, \qquad \mu=0.3. \] Therefore, \[ G = \frac{60}{2(1.3)} = \frac{60}{2.6} = 23.08\ \text{MPa}. \] Thus, \[ \boxed{G\approx23\ \text{MPa}.} \] Hence, \[ \boxed{(C)} \] is the correct answer.