The length of a wire is `4m`. Its length is increased by `2mm` when a force acts on it. The strain is

Options

A. `0.5xx10^(-3)`
B. `5xx10^(-3)`
C. `2xx10^(-3)`
D. `0.05`

Explanation

To find the strain in the wire, we can follow these steps:

### Step 1: Understand the concept of strain
Strain is defined as the ratio of the change in length (∆L) to the original length (L) of the wire. The formula for strain (E) is given by:

\[ E = \frac{\Delta L}{L} \]

### Step 2: Identify the given values
- Original length of the wire (L) = 4 meters
- Change in length (∆L) = 2 mm

### Step 3: Convert the change in length to meters
Since the original length is in meters, we need to convert the change in length from millimeters to meters.

\[ \Delta L = 2 \text{ mm} = 2 \times 10^{-3} \text{ m} \]

### Step 4: Substitute the values into the strain formula
Now we can substitute the values of ∆L and L into the strain formula:

\[ E = \frac{\Delta L}{L} = \frac{2 \times 10^{-3} \text{ m}}{4 \text{ m}} \]

### Step 5: Calculate the strain
Now we perform the division:

\[ E = \frac{2 \times 10^{-3}}{4} = 0.5 \times 10^{-3} \]

### Step 6: Express the answer in standard form
We can express the strain in standard form:

\[ E = 5 \times 10^{-4} \]

### Final Answer:
The strain in the wire is \( 5 \times 10^{-4} \).

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