Modulus of rigidity of a liquid

The correct answer is Zero.

Step-by-step Explanation:

1. Understanding Modulus of Rigidity:
The modulus of rigidity (also known as the shear modulus), denoted by $\eta$ or $G$, is a measure of a material's resistance to shear deformation (a change in shape without a change in volume). It is mathematically defined as the ratio of shear stress (${\sigma }_s$) to shear strain ($\theta$):
$\eta =\frac{\text{Shear Stress}}{\text{Shear Strain}}$

2. Behavior of Liquids under Shear Stress:
Unlike solids, liquids (and fluids in general) cannot support static shear stress. When a tangential force (shear stress) is applied to the surface of a liquid, the liquid starts to flow and continues to deform indefinitely as long as the stress is applied.

3. Evaluating the Modulus:
Because a liquid at rest cannot resist any shear force, its static shear stress is zero (${\sigma }_s=0$) for any deformation. Consequently, substituting this into the formula gives:
$\eta =\frac{0}{\text{Shear Strain}}=0$

Thus, the modulus of rigidity of a liquid is zero.