Identify the wrong statement from the following

Options

A. If the length of a spring is halved, the time period of each part becomes `(1)/(sqrt(2))` times the original
B. The effective spring constant K of springs in parallel is given by `(1)/(K)=(1)/(K_(1))+(1)/(K_(2))+…`
C. The time period of a stiffer spring is less than that of a soft spring
D. The spring constant is inversely proportional to the spring length

Explanation

To identify the wrong statement from the provided options, we need to analyze each statement carefully based on the principles of oscillations and spring mechanics.

### Step-by-Step Solution:

1. **Understanding the Time Period of a Spring**:
The time period \( T \) of a spring-mass system is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass attached to the spring and \( k \) is the spring constant.

2. **Effect of Cutting a Spring**:
When a spring is cut in half, the spring constant \( k \) of each half becomes double that of the original spring. This is because the spring constant is inversely proportional to the length of the spring. Therefore, if the length is halved, the new spring constant \( k' \) is:
\[ k' = 2k \]
Consequently, the time period of each half becomes:
\[ T' = 2\pi \sqrt{\frac{m}{k'}} = 2\pi \sqrt{\frac{m}{2k}} = \frac{T}{\sqrt{2}} \]
This means that the time period of each part becomes \( \frac{1}{\sqrt{2}} \) of the original time period, which is correct.

3. **Effective Spring Constant for Springs in Parallel**:
For springs arranged in parallel, the effective spring constant \( k_{eff} \) is given by:
\[ k_{eff} = k_1 + k_2 \]
This means that the total spring constant increases when springs are added in parallel, leading to a shorter time period.

4. **Analyzing the Statements**:
- **Option A**: If the length of the spring is halved, the period of each part becomes \( \frac{1}{\sqrt{2}} \) of the original. This statement is **correct**.
- **Option B**: The effective spring constant \( k \) of springs in parallel is given by \( \frac{1}{k} \). This statement is **incorrect** because the correct formula is \( k_{eff} = k_1 + k_2 \).
- **Option C**: The time period of a stiffer spring is less than that of a softer spring, which is **correct**.
- **Option D**: The effective spring constant for springs in parallel is \( k_{eff} = k_1 + k_2 \), which is also **correct**.

5. **Conclusion**:
The wrong statement is **Option B**, which incorrectly states that the effective spring constant for springs in parallel is given by \( \frac{1}{k} \).

### Final Answer:
The wrong statement is **Option B**.