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EEJ MAIN Physics QUESTION #7104
Question 1
Which of the following is the correct relationship between Young's modulus ($Y$), bulk modulus ($K$), and modulus of rigidity ($\eta$)? [cite: 487, 488]
  • $Y = \frac{9K\eta}{3K-\eta}$
  • $Y = \frac{9K\eta}{2\eta+3K}$
  • $K = \frac{Y\eta}{9\eta-3Y}$✔️
  • $\eta = \frac{3YK}{9K+Y}$
Correct Answer Explanation

The general relationship is $\frac{9}{Y} = \frac{3}{\eta} + \frac{1}{K}$.

  • Rearranging for $K$: $\frac{1}{K} = \frac{9}{Y} - \frac{3}{\eta} = \frac{9\eta - 3Y}{Y\eta}$
  • Thus, $K = \frac{Y\eta}{9\eta - 3Y}$[cite: 492].