Question

For a tissue with Young’s modulus 4 kPa and shear modulus 1.5 kPa, what is the value of the Poisson’s ratio?

• A. \( \frac{1}{5} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{1}{2} \)

Hint:

To calculate Poisson's ratio from Young's modulus and shear modulus, use the formula \( \nu = \frac{E}{2G} - 1 \).

Answer 1

The Correct Option is B

The relationship between Young's modulus \( E \), shear modulus \( G \), and Poisson’s ratio \( \nu \) is given by the formula: \[ E = 2G(1 + \nu) \] where:
\( E \) is Young's modulus,
\( G \) is the shear modulus,
\( \nu \) is Poisson's ratio.
Step 1: Rearranging the formula to solve for Poisson's ratio: \[ \nu = \frac{E}{2G} - 1 \] Step 2: Substituting the given values: Given \( E = 4 \, {kPa} \) and \( G = 1.5 \, {kPa} \), we substitute these values into the equation: \[ \nu = \frac{4}{2 \times 1.5} - 1 = \frac{4}{3} - 1 = \frac{1}{3} \] Step 3: Conclusion. The value of Poisson’s ratio is \( \frac{1}{3} \).