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For common metals such as aluminium and copper, which sequence correctly represents the relative magnitudes of the elastic moduli?

1. Young’s modulus < shear modulus < bulk modulus.
2. Bulk modulus < shear modulus < Young’s modulus.
3. Shear modulus < Young’s modulus < bulk modulus.
4. Bulk modulus < Young’s modulus < shear modulus.

Correct answer: Shear modulus < Young’s modulus < bulk modulus.

Solution

For common metals the shear modulus is smallest, then Young's modulus, then the bulk modulus (e.g. copper: G~48, Y~117, K~140 GPa; aluminium: G~26, Y~70, K~76 GPa). So shear modulus < Young's modulus < bulk modulus.

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