Searle's method is used to determine

Options

A. bulk modulus
B. compressibility
C. density of material
D. young's modulus

Explanation

**Step-by-Step Solution:**

1. **Understanding Searle's Method**: Searle's method is primarily used to determine the Young's modulus of materials. Young's modulus is a measure of the stiffness of a solid material.

2. **Setup of the Experiment**: In Searle's method, a circular wire is used. The wire is subjected to a tensile load, and its length and diameter are measured accurately.

3. **Applying the Formula for Stress and Strain**:
- **Stress (σ)** is defined as the force (F) applied per unit area (A). For a circular wire, the area can be calculated as:
\[ A = \frac{\pi d^2}{4} \]
Therefore, the stress can be expressed as:
\[ \sigma = \frac{F}{A} = \frac{4F}{\pi d^2} \]

- **Strain (ε)** is defined as the change in length (ΔL) divided by the original length (L):
\[ \epsilon = \frac{\Delta L}{L} \]

4. **Hooke's Law**: According to Hooke's law, stress is proportional to strain within the elastic limit:
\[ \sigma = E \cdot \epsilon \]
where E is the Young's modulus.

5. **Combining the Equations**: By substituting the expressions for stress and strain into Hooke's law, we get:
\[ \frac{4F}{\pi d^2} = E \cdot \frac{\Delta L}{L} \]

6. **Relative Error Calculation**: To find the relative error in the measurement of Young's modulus, we can express it as:
\[ \frac{\Delta E}{E} = \frac{\Delta L}{L} + 2 \frac{\Delta d}{d} \]
where ΔE is the change in Young's modulus, ΔL is the change in length, and Δd is the change in diameter.

7. **Conclusion**: Thus, Searle's method is specifically used for determining Young's modulus of materials by measuring the change in length and diameter of a wire under tensile stress.