A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is:

Options

A. 16 J
B. 8 J
C. 32 J
D. 24 J

Explanation

To solve the problem of finding the work done in extending a spring from 5 cm to 15 cm, we can follow these steps:

### Step 1: Understand the formula for work done on a spring
The work done (W) in extending a spring can be calculated using the formula:
\[ W = \frac{1}{2} k (x_2^2 - x_1^2) \]
where:
- \( k \) is the force constant of the spring (in N/m),
- \( x_1 \) is the initial extension (in m),
- \( x_2 \) is the final extension (in m).

### Step 2: Convert the extensions from centimeters to meters
The extensions given are in centimeters, so we need to convert them to meters:
- \( x_1 = 5 \, \text{cm} = 0.05 \, \text{m} \)
- \( x_2 = 15 \, \text{cm} = 0.15 \, \text{m} \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the work done formula:
- \( k = 800 \, \text{N/m} \)
- \( x_1 = 0.05 \, \text{m} \)
- \( x_2 = 0.15 \, \text{m} \)

Substituting these values into the formula gives:
\[ W = \frac{1}{2} \times 800 \times (0.15^2 - 0.05^2) \]

### Step 4: Calculate the squares of the extensions
Now we calculate the squares:
- \( 0.15^2 = 0.0225 \)
- \( 0.05^2 = 0.0025 \)

### Step 5: Substitute the squared values back into the formula
Now substitute these squared values back into the equation:
\[ W = \frac{1}{2} \times 800 \times (0.0225 - 0.0025) \]
\[ W = \frac{1}{2} \times 800 \times 0.02 \]

### Step 6: Calculate the work done
Now we can calculate the work done:
\[ W = \frac{1}{2} \times 800 \times 0.02 \]
\[ W = 400 \times 0.02 \]
\[ W = 8 \, \text{J} \]

### Final Answer
The work done in extending the spring from 5 cm to 15 cm is **8 Joules**.

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