The ratio of shearing stress to the shearing strain is defined as

Options

A. Young's modulus
B. bulk modulus
C. shear modulus
D. compressibility

Explanation

To solve the question regarding the ratio of shearing stress to shearing strain, we can follow these steps:

### Step 1: Understand the Definitions
- **Shearing Stress (τ)**: This is defined as the force (F) applied parallel to the surface of a material divided by the area (A) over which the force is applied. Mathematically, it is expressed as:
\[ \tau = \frac{F}{A} \]

- **Shearing Strain (γ)**: This is defined as the change in the shape of the material due to the applied stress. It is the ratio of the displacement (x) to the height (h) of the material. Mathematically, it can be expressed as:
\[ \gamma = \frac{x}{h} \]

### Step 2: Establish the Relationship
- The ratio of shearing stress to shearing strain is given by:
\[ \text{Shear Modulus (G)} = \frac{\text{Shearing Stress}}{\text{Shearing Strain}} = \frac{\tau}{\gamma} \]

### Step 3: Identify the Correct Term
- The term that describes this ratio is known as the **Shear Modulus**. It quantifies the material's response to shearing stress and is a measure of its rigidity.

### Conclusion
- Therefore, the ratio of shearing stress to shearing strain is defined as the **Shear Modulus**.

### Final Answer
The ratio of shearing stress to shearing strain is defined as **Shear Modulus**.

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