If a spring has time period T, and is cut into (n) equal parts, then the time period of each part will be.

Options

A. (a)`Tsqrt(n)`
B. (b)`T/sqrt(n)`
C. (c)nT
D. (d)T

Explanation

To solve the problem of finding the time period of each part of a spring when it is cut into \( n \) equal parts, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the original length of the spring be \( L \).
- The spring constant of the original spring is denoted as \( k \).
- The time period of the original spring is given as \( T \).

2. **Relate Time Period to Spring Constant**:
- The time period \( T \) of a spring is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- Here, \( m \) is the mass attached to the spring. For simplicity, we will consider the mass constant for each part.

3. **Cut the Spring into \( n \) Equal Parts**:
- When the spring is cut into \( n \) equal parts, the length of each part becomes:
\[ L' = \frac{L}{n} \]

4. **Determine the New Spring Constant**:
- The spring constant \( k' \) of each part is related to the original spring constant \( k \) by the formula:
\[ k' = n \cdot k \]
- This is because the spring constant is inversely proportional to the length of the spring. When the length decreases, the spring constant increases.

5. **Calculate the New Time Period**:
- The time period \( T' \) for each part of the spring can be expressed as:
\[ T' = 2\pi \sqrt{\frac{m}{k'}} \]
- Substituting \( k' = n \cdot k \) into the equation gives:
\[ T' = 2\pi \sqrt{\frac{m}{n \cdot k}} \]

6. **Relate the New Time Period to the Original Time Period**:
- We can express \( T' \) in terms of the original time period \( T \):
\[ T' = \frac{T}{\sqrt{n}} \]
- This shows that the time period of each part of the spring is inversely proportional to the square root of the number of parts \( n \).

### Final Answer:
The time period of each part of the spring when it is cut into \( n \) equal parts is:
\[ T' = \frac{T}{\sqrt{n}} \]