For an ideal iquid

Options

A. bulk modulus is infinite and shear modulus is zero.
B. bulk modulus is zero and shear modulus is inifinite.
C. bulk moduius is infinite and shear modulus is also infinite
D. bulk modulus is zero and shear modulus is also zero.

Explanation

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

### Step-by-Step Solution:

1. **Understanding Ideal Liquids**:
- An ideal liquid is defined as an incompressible fluid with no viscosity. This means that it does not change its volume under pressure and does not resist shear stress.

2. **Bulk Modulus (B)**:
- The bulk modulus is defined as the ratio of pressure increase to the relative decrease in volume:
\[ B = -\frac{P}{\Delta V / V} \]
- For an ideal liquid, since it is incompressible, the change in volume (\(\Delta V\)) is zero. Therefore:
\[ B = -\frac{P}{0} \rightarrow \text{infinity} \]

3. **Shear Modulus (G)**:
- The shear modulus is defined as the ratio of shear stress to shear strain:
\[ G = \frac{\text{Shear Stress}}{\text{Shear Strain}} \]
- For an ideal liquid, when shear stress is applied, the liquid does not deform in a way that creates shear strain; hence the shear strain is effectively zero. Therefore:
\[ G = \frac{\text{Shear Stress}}{0} \rightarrow 0 \]

4. **Conclusion**:
- From the above analysis, we conclude that for an ideal liquid:
- Bulk modulus \(B\) is infinite.
- Shear modulus \(G\) is zero.
- Thus, the correct option is: **Bulk modulus is infinite and shear modulus is zero**.

### Final Answer:
The correct option is: **Bulk modulus is infinite and shear modulus is zero.**

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