Select the incorrect option

Options

A. a. The Young's modulus and modulus of rigidity exist only for solids
B. b. The value of modulus of elasticity is independent of the magnitude of stress and strain
C. c. The value of modulus of elasticity depends only on the nature of material of the body
D. d. Only gases cannot exhibit a shearing stress

Answer

To solve the question of selecting the incorrect option regarding the properties of solids, we will analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** Young's modulus and modulus of rigidity exist only for solids.

**Explanation:** Young's modulus (Y) is defined as the ratio of longitudinal stress to longitudinal strain, while the modulus of rigidity (also known as shear modulus) is defined as the ratio of shear stress to shear strain. Both of these moduli are properties that characterize the mechanical behavior of solids. In liquids and gases, these concepts do not apply in the same way since they do not maintain a fixed shape under stress.

**Conclusion:** This statement is **true**.

### Step 2: Analyze Option B
**Statement:** The value of modulus of elasticity is independent of the magnitude of stress and strain.

**Explanation:** The modulus of elasticity is indeed a property of the material that describes its ability to deform elastically when a stress is applied. However, it is important to note that while the modulus itself is a constant for a given material, the actual stress and strain values can vary. The modulus of elasticity is defined within the limits of proportionality (Hooke's Law), meaning it is valid only up to a certain stress level. Beyond that, the relationship may not hold true.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze Option C
**Statement:** The value of modulus of elasticity depends on the nature of the material of the body.

**Explanation:** The modulus of elasticity is indeed a characteristic property of materials. Different materials (like rubber, steel, etc.) have different moduli of elasticity, reflecting their different abilities to deform under stress.

**Conclusion:** This statement is **true**.

### Step 4: Analyze Option D
**Statement:** Only gases cannot exhibit a shearing stress.

**Explanation:** Shearing stress is defined as the force per unit area acting parallel to the surface. Both liquids and gases can exhibit shear stress. In fact, when a fluid flows, it can exert shear stress at the boundary. Therefore, the statement that only gases cannot exhibit shearing stress is incorrect because liquids can also exhibit shear stress.

**Conclusion:** This statement is **incorrect**.

### Final Conclusion
After analyzing all the options, we find that:
- Option A: True
- Option B: Incorrect
- Option C: True
- Option D: Incorrect

The incorrect options are **B** and **D**. However, since the question asks for a single incorrect option, we select **Option B** as the primary incorrect statement.

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