Modulus of rigidity of a Ideal liquid

Options

A. infinity
B. zero
C. unity
D. some finite small non-zero constant value

Explanation

To determine the modulus of rigidity of an ideal liquid, we can follow these steps:

### Step 1: Understand the definition of modulus of rigidity
The modulus of rigidity (also known as shear modulus) is defined as the ratio of shear stress to shear strain.

### Step 2: Define shear stress and shear strain
- **Shear Stress** (\( \tau \)) is defined as the force (\( F \)) applied per unit area (\( A \)):
\[ \tau = \frac{F}{A} \]
- **Shear Strain** (\( \gamma \)) is defined as the change in position (\( \Delta x \)) divided by the original length (\( L \)):
\[ \gamma = \frac{\Delta x}{L} \]

### Step 3: Analyze the behavior of an ideal liquid
An ideal liquid is characterized by the absence of viscosity, which means there are no internal frictional forces acting between the layers of the liquid. This leads to the following conclusions:
- For an ideal liquid, when a shear force is applied, the liquid does not resist the deformation in a way that produces shear stress.
- Therefore, the shear stress (\( \tau \)) becomes 0.

### Step 4: Determine shear strain in an ideal liquid
Since there is no resistance to the applied shear force, even a small force can lead to a large displacement. However, because there is no shear stress, we can conclude that:
- Shear strain (\( \gamma \)) can be large, but since shear stress is 0, the modulus of rigidity will still be evaluated.

### Step 5: Calculate the modulus of rigidity
Using the definition of modulus of rigidity:
\[ G = \frac{\tau}{\gamma} \]
Since \( \tau = 0 \):
\[ G = \frac{0}{\gamma} = 0 \]

### Conclusion
The modulus of rigidity of an ideal liquid is:
\[ \text{Modulus of rigidity} = 0 \]
Thus, the correct answer is **Option 2: 0**.

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