Which of the following apparatus is used to determine the Young's modulus of the material of a gives given wires?

Options

A. Searle
B. sonometer
C. Metre bridge
D. Resonance tube

Explanation

To determine the Young's modulus of the material of a given wire, we need to identify the appropriate apparatus from the options provided. Here’s a step-by-step solution:

### Step 1: Understanding Young's Modulus
Young's modulus (E) is a measure of the stiffness of a material and is defined as the ratio of tensile stress to tensile strain. To measure it, we typically need to apply a known force to a wire and measure the resulting elongation.

### Step 2: Evaluating the Options
We need to evaluate the apparatus listed in the question to see which one is specifically designed for measuring Young's modulus.

1. **Searle's apparatus**: This apparatus is specifically designed for measuring Young's modulus by applying a known load to a wire and measuring the elongation.

2. **Sonometer**: This device is used to measure the frequency of vibration of a wire under tension and can also be used to determine the tension in the wire, but it is not primarily used for measuring Young's modulus.

3. **Meter Bridge**: This apparatus is used to measure unknown electrical resistances using the principle of a Wheatstone bridge. It does not relate to measuring Young's modulus.

4. **Resonance Tube**: This apparatus is used to determine the speed of sound in air or other gases and is not related to measuring the properties of solid materials like Young's modulus.

### Step 3: Conclusion
From the evaluation, we can conclude that the correct apparatus for determining the Young's modulus of the material of a given wire is **Searle's apparatus**.

### Final Answer
The apparatus used to determine the Young's modulus of the material of a given wire is **Searle's apparatus**.

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