(A): Solids can support both longitudinal and transverse waves but only mechanical longitudinal waves can propagate in gases.
(R): For the propagation of mechanical transverse waves, medium must also necessarily have the property of rigidity.

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 analyze the given statements, we will go through them step by step.

### Step 1: Analyze Statement A
**Assertion (A):** "Solids can support both longitudinal and transverse waves but only mechanical longitudinal waves can propagate in gases."

- **Longitudinal Waves:** These are waves where the particle displacement is parallel to the direction of wave propagation. Both solids and gases can support longitudinal waves because they can compress and expand.

- **Transverse Waves:** These are waves where the particle displacement is perpendicular to the direction of wave propagation. Solids can support transverse waves due to their rigidity. However, gases do not have the property of rigidity, which prevents the propagation of transverse waves.

**Conclusion for A:** The first part of the assertion is true (solids can support both types of waves), and the second part is also true (only longitudinal waves can propagate in gases). Therefore, Statement A is true.

### Step 2: Analyze Statement R
**Reason (R):** "For the propagation of mechanical transverse waves, the medium must also necessarily have the property of rigidity."

- **Rigidity:** This is the ability of a medium to resist deformation. Transverse waves require a medium that can maintain its shape when a force is applied, which is a characteristic of rigid materials.

**Conclusion for R:** This statement is true because transverse waves cannot propagate in a medium that lacks rigidity, such as gases.

### Step 3: Determine the Relationship Between A and R
Now, we need to determine if R is the correct explanation for A.

- Since A states that solids can support both types of waves and gases can only support longitudinal waves, and R explains that rigidity is necessary for transverse wave propagation, R correctly explains why gases cannot support transverse waves.

### Final Conclusion
Both statements A and R are true, and R is the correct explanation of A.

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

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