Modulus of rigidity of ideal liquids is

The correct option is zero.

Understanding Modulus of Rigidity:
The modulus of rigidity (also known as the shear modulus, commonly denoted by $\eta$ or $G$) measures a substance's resistance to shear flow or shear deformation. It is defined as the ratio of shear stress to shear strain:

$\eta =\frac{\text{Shear Stress}}{\text{Shear Strain}}$

Behavior of Ideal Liquids:
1. Fluids (liquids and gases) do not have a fixed shape and cannot withstand static shear stress. When a tangential (shear) force is applied to a fluid, it undergoes continuous deformation and begins to flow.
2. An ideal liquid is defined as a fluid that is incompressible and has zero viscosity (no internal friction or resistance to flow).
3. Because an ideal liquid has zero viscosity, it offers no resistance whatsoever to shear deformation. Consequently, the shear stress in an ideal liquid is always zero:

$\text{Shear Stress}=0$

Substituting this value into the formula for the modulus of rigidity:

$\eta =\frac{0}{\text{Shear Strain}}=0$

Therefore, the modulus of rigidity of an ideal liquid is always zero.