Question

If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

• A. $Y = \frac{9K\eta}{2\eta + 3K} \text{ N/m}^2$
• B. $Y = \frac{9K\eta}{3K - \eta} \text{ N/m}^2$
• C. $K = \frac{Y\eta}{9\eta - 3Y} \text{ N/m}^2$
• D. $\eta = \frac{3YK}{9K + Y} \text{ N/m}^2$

Hint:

To remember the relation easily, use the "9, 3, 1" rule: $\frac{9}{Y} = \frac{3}{\eta} + \frac{1}{K}$.

Answer 1

The Correct Option is C

Step 1: The standard relationship between moduli is $\frac{9}{Y} = \frac{3}{\eta} + \frac{1}{K}$.
Step 2: Rearranging to find $K$: $\frac{1}{K} = \frac{9}{Y} - \frac{3}{\eta} = \frac{9\eta - 3Y}{Y\eta}$.
Step 3: Taking the reciprocal: $K = \frac{Y\eta}{9\eta - 3Y}$.