(A): Mechanical transverse waves can propagate only in medium with shear modulus of elasticity
(B) : Longitudinal waves need bulk modulus of elasticity and are therefore possible in all media, solids, liquids and gases

Options

A. Both A and B are true
B. Both A and B are false
C. A is true, B is false
D. A is false, B is true

Answer

To solve the question, let's analyze the two statements one by one.

### Step 1: Analyze Statement A
**Statement A:** "Mechanical transverse waves can propagate only in medium with shear modulus of elasticity."

- **Understanding Transverse Waves:** Transverse waves are waves where the particle displacement is perpendicular to the direction of wave propagation.
- **Medium Requirement:** Transverse waves require a medium that can support shear stress. This is because shear modulus of elasticity is a measure of a material's ability to resist shear deformation.
- **Conclusion for Statement A:** Transverse waves can only propagate in solids (which have shear modulus) and not in fluids (liquids and gases). Therefore, this statement is **True**.

### Step 2: Analyze Statement B
**Statement B:** "Longitudinal waves need bulk modulus of elasticity and are therefore possible in all media, solids, liquids, and gases."

- **Understanding Longitudinal Waves:** Longitudinal waves are waves where the particle displacement is parallel to the direction of wave propagation.
- **Medium Requirement:** Longitudinal waves require a medium that can compress and expand, which is characterized by bulk modulus of elasticity.
- **Conclusion for Statement B:** Since solids, liquids, and gases all possess bulk modulus, longitudinal waves can propagate through all these states of matter. Therefore, this statement is also **True**.

### Final Conclusion
Both statements A and B are true.

### Answer
The correct option is: **Both A and B are true.**

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