The length of a wire increases by `1%` on loading 2 kg wt on it. The linear strain in the wire is,

Options

A. 1
B. 0.01
C. 0.1
D. 0.001

Explanation

To find the linear strain in the wire when it increases in length by 1% upon loading a 2 kg weight, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
We know that the length of the wire increases by 1% when a weight of 2 kg is applied. We need to find the linear strain in the wire.

2. **Define Initial Length**:
Let the initial length of the wire be \( L \).

3. **Calculate the Increase in Length**:
The increase in length, denoted as \( \Delta L \), can be calculated based on the percentage increase. Since the length increases by 1%, we have:
\[ \Delta L = \frac{1}{100} \times L = 0.01L \]

4. **Formula for Linear Strain**:
Linear strain (\( \epsilon \)) is defined as the change in length divided by the original length:
\[ \epsilon = \frac{\Delta L}{L} \]

5. **Substituting the Values**:
Substitute \( \Delta L \) into the strain formula:
\[ \epsilon = \frac{0.01L}{L} \]

6. **Simplifying the Expression**:
The \( L \) in the numerator and denominator cancels out:
\[ \epsilon = 0.01 \]

7. **Final Answer**:
Therefore, the linear strain in the wire is:
\[ \epsilon = 0.01 \text{ (dimensionless)} \]