What will be the stress required to double the length of a wire of Young's modulus Y?

Options

A. Y
B. 2Y
C. 3Y
D. 4Y

Explanation

To find the stress required to double the length of a wire with a given Young's modulus \( Y \), we can follow these steps:

### Step 1: Understand the relationship between stress, strain, and Young's modulus
Young's modulus \( Y \) is defined as the ratio of stress \( \sigma \) to strain \( \epsilon \):
\[ Y = \frac{\sigma}{\epsilon} \]
where:
- \( \sigma \) is the stress applied to the wire,
- \( \epsilon \) is the strain experienced by the wire.

### Step 2: Define strain in terms of length
Strain \( \epsilon \) is defined as the change in length divided by the original length. If we want to double the length of the wire, the change in length \( \Delta L \) is equal to the original length \( L \):
\[ \epsilon = \frac{\Delta L}{L} = \frac{L}{L} = 1 \]

### Step 3: Substitute strain into the Young's modulus equation
Now that we know the strain \( \epsilon = 1 \), we can substitute this value into the Young's modulus equation:
\[ Y = \frac{\sigma}{1} \implies \sigma = Y \]

### Step 4: Conclusion
The stress required to double the length of the wire is equal to the Young's modulus \( Y \):
\[ \sigma = Y \]

### Final Answer
The stress required to double the length of the wire is \( Y \).

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