A spring with 10 coils has spring constant k. It is exactly cut into two halves, then each of these new springs will have a spring constant

Options

A. K/2
B. 3k/2
C. 2k
D. 3 k

Answer

To solve the problem of determining the spring constant of the new springs after a spring with 10 coils and spring constant \( k \) is cut into two halves, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Original Spring**:
- The original spring has a spring constant \( k \) and a length \( L \).
- The relationship between the spring constant \( k \), the length \( L \), and the new spring constant \( k' \) after cutting is important.

2. **Cut the Spring**:
- When the spring is cut into two equal halves, each half will have a new length of \( L/2 \).

3. **Use the Spring Constant Formula**:
- The spring constant is inversely proportional to the length of the spring. This means that if the length of the spring is halved, the spring constant will double.
- Mathematically, this can be expressed as:
\[ k' = \frac{k \cdot L}{L/2} \]

4. **Simplify the Equation**:
- Substitute \( L/2 \) into the equation:
\[ k' = \frac{k \cdot L}{L/2} = k \cdot \frac{L}{L} \cdot 2 = 2k \]

5. **Conclusion**:
- Therefore, the spring constant of each of the new springs after cutting the original spring in half is \( 2k \).

### Final Answer:
The new spring constant \( k' \) for each half of the spring is \( 2k \).