(A): Only longitudinal waves can propagate through a gas.
(R): Gases have only bulk modulus.

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states: "Only longitudinal waves can propagate through a gas."

- **Understanding Longitudinal Waves**: Longitudinal waves are waves in which the particle displacement is parallel to the direction of wave propagation. Sound waves in gases are a prime example of longitudinal waves.
- **Behavior of Gases**: Gases can support longitudinal waves because they can compress and expand, which is essential for the propagation of sound. However, gases do not have the rigidity required to support transverse waves (where particle displacement is perpendicular to the direction of wave propagation).

**Conclusion for A**: The assertion is true because only longitudinal waves can propagate through a gas.

### Step 2: Analyze the Reason (R)
The reason states: "Gases have only bulk modulus."

- **Understanding Bulk Modulus**: Bulk modulus is a measure of a substance's resistance to uniform compression. It is relevant for gases, as they can be compressed and have volume.
- **Modulus of Rigidity**: This modulus is relevant for solids and is not applicable to gases. Gases do not exhibit rigidity, which is why they cannot support transverse waves.

**Conclusion for R**: The reason is true because gases indeed have only bulk modulus and do not have modulus of rigidity.

### Step 3: Determine the Relationship Between A and R
Now we need to check if the reason (R) correctly explains the assertion (A).

- The assertion is true because longitudinal waves can propagate through gases due to the presence of bulk modulus.
- The reason is also true, and it provides a valid explanation for why only longitudinal waves can propagate through gases, as gases lack modulus of rigidity.

### Final Conclusion
Both the assertion (A) and the reason (R) are true, and R is the correct explanation of A. Therefore, the correct answer is:

**Both A and R are true, and R is the correct explanation of A.**

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