A wire of length 2.5 m has a percentage strain of 0.012% under a tensile force. The extension produce in the wire will be

Options

A. 0.03 mm
B. 0.3 mm
C. 0.3 mm
D. 0.03 m

Explanation

To find the extension produced in the wire, we can use the relationship between strain, extension, and original length. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Length of the wire (L) = 2.5 m
- Percentage strain = 0.012%

### Step 2: Convert percentage strain to decimal
Percentage strain is given as 0.012%. To convert this to a decimal form, we divide by 100:
\[ \text{Strain} = \frac{0.012}{100} = 0.00012 \]

### Step 3: Use the formula for strain
Strain (ε) is defined as the ratio of the extension (ΔL) to the original length (L):
\[ \text{Strain} = \frac{\Delta L}{L} \]
Rearranging this formula gives us:
\[ \Delta L = \text{Strain} \times L \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have into the formula:
\[ \Delta L = 0.00012 \times 2.5 \]

### Step 5: Calculate the extension
Now, performing the multiplication:
\[ \Delta L = 0.00012 \times 2.5 = 0.0003 \text{ m} \]

### Step 6: Convert the extension to millimeters
To convert meters to millimeters, we multiply by 1000:
\[ \Delta L = 0.0003 \text{ m} \times 1000 = 0.3 \text{ mm} \]

### Final Answer
The extension produced in the wire is **0.3 mm**.

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