Question

Meaning of Young's modulus and bulk modulus with mathematical expression​

Answer 1

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Young's modulus is the ratio of normal stress to the longitudinal strain

it is denoted by Y

$\large \mathtt{ \fbox{ Young's \: modulus = \frac{normal \: stress}{longitudinal \: strain}} }$

Bulk modulus is the ratio of normal stress to the volumetric strain

It is denoted by K

$\large \mathtt{ \fbox{ Bulk \: modulus = \frac{normal \: stress}{volumetric \: strain}} }$

$\large \red{ \star }$Extra information :

Strain is the ratio of change in configuration to the original configuration

$\sf \large \fbox {</p><p> Strain = \frac{change \: in \: configuration }{ original \: configuration } }$

Longitudinal strain is the ratio of change in length to the original length

$\sf \large \fbox {Longitudinal \: strain = \frac{ \triangle L }{L } }$

Volumetric strain is the ratio of change in volume to the original volume

$\sf \large \fbox {Volumetric \: strain = \frac{ \triangle V }{V } }$