A spring of spring constant k is cut in three equal pieces. The spring constant of each part will be

Options

A. `(k)/(3)`
B. `3k`
C. `k`
D. `(k)/(6)`

Answer

To solve the problem of finding the spring constant of each part when a spring of spring constant \( k \) is cut into three equal pieces, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Condition**:
- We have a spring of length \( L \) and spring constant \( k \).
- The relationship between the spring constant \( k \) and the length \( L \) is given by the formula:
\[ k \cdot L = \text{constant} \]

2. **Cut the Spring**:
- The spring is cut into three equal pieces. Therefore, the length of each piece becomes:
\[ \text{Length of each piece} = \frac{L}{3} \]

3. **Define the New Spring Constant**:
- Let the new spring constant of each piece be \( k' \).
- According to the spring constant relationship, for each piece, we have:
\[ k' \cdot \left(\frac{L}{3}\right) = \text{constant} \]

4. **Set Up the Equation**:
- For the original spring, the relationship can be expressed as:
\[ k \cdot L = k' \cdot \left(\frac{L}{3}\right) \]

5. **Solve for the New Spring Constant**:
- Rearranging the equation gives:
\[ k' = k \cdot \frac{L}{\frac{L}{3}} = k \cdot 3 = 3k \]

6. **Conclusion**:
- The spring constant of each of the three equal pieces is:
\[ k' = 3k \]

### Final Answer:
The spring constant of each part will be \( 3k \).