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Let Y, K and eta denote the Young's modulus, bulk modulus and rigidity (shear) modulus of a material. If the rigidity modulus equals twice the bulk modulus (eta = 2K), find the relation for Y.

1. Y = 5K/18
2. Y = 5eta/9
3. Y = 9K/5
4. Y = 18K/5

Correct answer: Y = 18K/5

Solution

From 9/Y = 1/K + 3/eta with eta = 2K, the right side becomes 5/(2K), giving Y = 18K/5.

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