Which of the following is correct?

Options

A. Gases have fixed density
B. Liquids are highly compressible
C. Liquids have small shear modulus
D. Gases have high shear modulus

Answer

To determine which of the given statements is correct, we will analyze each statement one by one.

### Step 1: Analyze the first statement - "Gases have fixed density."
- **Explanation**: Density is defined as mass per unit volume (Density = Mass/Volume). Gases do not have a fixed volume; they expand to fill the entire container they are in. Therefore, the density of a gas can change depending on the volume it occupies.
- **Conclusion**: This statement is **false**.

### Step 2: Analyze the second statement - "Liquids are highly compressible."
- **Explanation**: Liquids are indeed compressible, but their compressibility is much lower compared to gases. The molecules in liquids are closely packed, which means that applying pressure results in only a small change in volume.
- **Conclusion**: This statement is **false**.

### Step 3: Analyze the third statement - "Liquids have small shear modulus."
- **Explanation**: Shear modulus (η) is defined as the ratio of shear stress to shear strain. In liquids, when a shear force is applied, the liquid flows rather than maintaining its shape. This results in a very small shear modulus, often considered to be approximately zero.
- **Conclusion**: This statement is **true**.

### Step 4: Analyze the fourth statement - "Gases have high shear modulus."
- **Explanation**: In gases, when a shear force is applied, the gas does not resist the deformation in the same way solids do; instead, it flows. Therefore, gases do not have a shear modulus, as there is no resistance to shear stress.
- **Conclusion**: This statement is **false**.

### Final Conclusion:
After analyzing all the statements, the only correct statement is:
- **C: Liquids have small shear modulus.**