A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1mm, then the work done in stretching the spring through 40 mm is

Options

A. 84 J
B. 68 J
C. 23 J
D. 8 J

Explanation

To solve the problem of calculating the work done in stretching a spring through 40 mm, we will follow these steps:

### Step 1: Understand the Given Data
- The natural length of the spring is 40 mm.
- A force of 10 N is required to stretch the spring by 1 mm.

### Step 2: Convert Units
- Convert the extension from mm to meters for standard SI units.
\[ 40 \text{ mm} = 40 \times 10^{-3} \text{ m} = 0.04 \text{ m} \]

### Step 3: Calculate the Spring Constant (k)
- The spring constant \( k \) can be calculated using Hooke's Law, which states:
\[ k = \frac{F}{x} \]
where \( F \) is the force applied and \( x \) is the extension.
- Here, \( F = 10 \text{ N} \) and \( x = 1 \text{ mm} = 1 \times 10^{-3} \text{ m} \).
\[ k = \frac{10 \text{ N}}{1 \times 10^{-3} \text{ m}} = 10^4 \text{ N/m} \]

### Step 4: Calculate the Work Done (W)
- The work done in stretching the spring can be calculated using the formula:
\[ W = \frac{1}{2} k x^2 \]
- Substitute the values of \( k \) and \( x \):
\[ W = \frac{1}{2} \times 10^4 \text{ N/m} \times (0.04 \text{ m})^2 \]
\[ W = \frac{1}{2} \times 10^4 \times 0.0016 \text{ m}^2 \]
\[ W = \frac{1}{2} \times 16 \text{ J} = 8 \text{ J} \]

### Final Answer
The work done in stretching the spring through 40 mm is **8 Joules**.

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