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In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is:       [JEE ONLINE 09-04-2014]

A)  Young’s modulus < shear modulus < bulk modulus.

B)  Bulk modulus < shear modulus < Young’s modulus

C)  Shear modulus < Young’s modulus < bulk modulus.

D)  Bulk modulus < Young’s modulus < shear modulus Correct Answer: C Solution : [c]

Poisson’s ratio,\[\text{ }\!\!\sigma\!\!\text{ }\,\text{=}\frac{\text{lateral}\,\text{strain( }\!\!\beta\!\!\text{ )}}{\text{longitudinal}\,\text{strain( }\!\!\alpha\!\!\text{ )}}\]

For material like copper, \[\text{ }\!\!\sigma\!\!\text{ }\,\text{=0}\text{.33}\]

And, \[y=3k(1-2\sigma )\]

Also,\[\frac{9}{y}=\frac{1}{k}+\frac{3}{n}\]                  \[y=2n(1+\sigma )\]

Hence, n < y < k