Explain Shear Modulus and Bulk Modulus.

(N/A) The ratio of shearing stress to the corresponding shearing strain is called the shear modulus of the material and is represented by $G$. It is also called the modulus of rigidity.
$G = \frac{\text{Shearing stress } (\sigma_s)}{\text{Shearing strain } (\theta)} = \frac{F/A}{\Delta x/L} = \frac{FL}{A \Delta x}$
For small angles,$\frac{\Delta x}{L} = \tan \theta \approx \theta$,so $G = \frac{F/A}{\theta} = \frac{F}{A \theta}$.
The shearing stress $\sigma_s$ can be expressed as $\sigma_s = G \times \theta$.
The $SI$ unit of shear modulus is $N m^{-2}$ or $Pa$.
Generally,the shear modulus is less than Young's modulus,and for most materials,$G \approx \frac{Y}{3}$.
When a body is submerged in a fluid,it undergoes hydraulic stress (equal in magnitude to the hydraulic pressure). This leads to a decrease in the volume of the body,producing a volume strain.
The ratio of hydraulic stress to the corresponding hydraulic strain is called the bulk modulus,denoted by $B$.
$B = -\frac{p}{\Delta V / V}$
The negative sign indicates that an increase in pressure leads to a decrease in volume (if $p > 0$,then $\Delta V < 0$). Thus,for a system in equilibrium,$B$ is always positive.
The $SI$ unit of bulk modulus is $N m^{-2}$ or $Pa$,and its dimensional formula is $[M^1 L^{-1} T^{-2}]$.