Physics · Young's modulus, bulk modulus and modulus of rigidity
represent respectively the young's modulus,bulk modulus and rigidity modulus of
\( \boldsymbol{Y}, \boldsymbol{k}, \boldsymbol{n} \) represent respectively the young's modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk modulus, then:
- A. \( Y=5 k / 18 \)
- B. \( Y=5 n / 9 \)
- C. \( Y=9 k / 5 \)
- D. \( Y=18 k / 5 \)
Step-by-step solution
Given n = 2k. Using the relation between elastic moduli: 1/Y = 1/(3k) + 1/(3n) = 1/(3k) + 1/(6k) = 1/(2k). Hence Y = 2k? Actually careful: The standard relation is 9/Y = 3/k + 1/n? Wait, correct formula: Y = 9kn/(3k+n). Substitute n=2k: Y = 9k(2k)/(3k+2k) = 18k²/(5k) = 18k/5.
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