For an ideal liquid :

Options

A. the shear modulus is infinite.
B. the shear modulus is zero
C. the bulk modulus is zero.
D. the bulk modulus is infinite.

Answer

To solve the question regarding the properties of an ideal liquid, we need to analyze the characteristics of an ideal liquid in terms of its bulk modulus and shear modulus.

### Step-by-Step Solution:

1. **Understanding Ideal Liquid**:
- An ideal liquid is one that is incompressible and has no viscosity. This means that it does not resist deformation and can flow freely.

2. **Bulk Modulus**:
- The bulk modulus (K) of a substance is defined as the measure of its resistance to uniform compression. It is mathematically expressed as:
\[ K = -V \frac{dP}{dV} \]
- For an ideal liquid, since it is incompressible, the change in volume (dV) is zero when pressure (P) is applied. Thus, the bulk modulus approaches infinity:
\[ K = \frac{1}{\text{Compressibility}} \rightarrow \infty \quad \text{(as compressibility approaches 0)} \]

3. **Shear Modulus**:
- The shear modulus (G) is a measure of a material's ability to resist shear deformation. For an ideal liquid, which has no viscosity, the layers of the liquid can slide over each other without any resistance.
- Mathematically, the shear modulus can be expressed as:
\[ G = \frac{\text{Shear Stress}}{\text{Shear Strain}} \]
- Since there is no viscosity in an ideal liquid, even a small applied force can cause an infinite displacement (Δx) of the layers. Therefore, the shear modulus tends to zero:
\[ G \rightarrow 0 \quad \text{(as shear strain becomes infinite)} \]

4. **Conclusion**:
- From the analysis, we conclude that for an ideal liquid:
- The bulk modulus is infinite.
- The shear modulus is zero.

### Final Answer:
- The correct conditions for an ideal liquid are:
- Bulk modulus is infinite.
- Shear modulus is zero.