When the load applied to stretch a wire is increased from 1kg-wt to 2kg-wt, the extention produced in the wire increases from 0.5 mm to 1mm. The work done in the extenstion of the wire is `(g = 10 m//s^(2))`

Options

A. `2.5 xx 10^(-3) J`
B. `1.87 xx 10^(-3) J`
C. `7.5 xx 10^(-3) J`
D. `1.5 xx 10^(-3) J`

Explanation

To find the work done in stretching the wire when the load is increased from 1 kg-wt to 2 kg-wt, we can follow these steps:

### Step 1: Convert the weights to forces
The force exerted by the weights can be calculated using the formula:
\[ F = m \cdot g \]
where \( g = 10 \, \text{m/s}^2 \).

- For the first weight (1 kg):
\[ F_1 = 1 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10 \, \text{N} \]

- For the second weight (2 kg):
\[ F_2 = 2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20 \, \text{N} \]

### Step 2: Convert the extensions to meters
The extensions given are in millimeters, so we need to convert them to meters:
- For the first extension (0.5 mm):
\[ \Delta L_1 = 0.5 \, \text{mm} = 0.5 \times 10^{-3} \, \text{m} = 0.0005 \, \text{m} \]

- For the second extension (1 mm):
\[ \Delta L_2 = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} = 0.001 \, \text{m} \]

### Step 3: Calculate the work done for each extension
The work done in stretching the wire can be calculated using the formula:
\[ W = \frac{1}{2} F \Delta L \]

- For the first extension (W1):
\[ W_1 = \frac{1}{2} F_1 \Delta L_1 = \frac{1}{2} \cdot 10 \, \text{N} \cdot 0.0005 \, \text{m} \]
\[ W_1 = \frac{1}{2} \cdot 10 \cdot 0.0005 = 0.0025 \, \text{J} \]

- For the second extension (W2):
\[ W_2 = \frac{1}{2} F_2 \Delta L_2 = \frac{1}{2} \cdot 20 \, \text{N} \cdot 0.001 \, \text{m} \]
\[ W_2 = \frac{1}{2} \cdot 20 \cdot 0.001 = 0.01 \, \text{J} \]

### Step 4: Calculate the work done during the extension
The work done during the extension when the load is increased from 1 kg-wt to 2 kg-wt is given by:
\[ W = W_2 - W_1 \]
\[ W = 0.01 \, \text{J} - 0.0025 \, \text{J} \]
\[ W = 0.0075 \, \text{J} \]

### Final Answer
The work done in the extension of the wire is:
\[ \boxed{0.0075 \, \text{J}} \]