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. `Tsqrtn`
B. `T//sqrtn`
C. `nT`
D. `T`

Explanation

To solve the problem, let's break it down step by step:

### Step 1: Understand the Time Period of a Spring
The time period \( T \) of a spring in simple harmonic motion is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where:
- \( m \) is the mass attached to the spring,
- \( k \) is the spring constant.

### Step 2: Consider the Effect of Cutting the Spring
When the spring is cut into \( n \) equal parts, each part will have a new spring constant. The spring constant \( k' \) of each part can be determined as follows:
- The spring constant of a spring is inversely proportional to its length. When the original spring is cut into \( n \) parts, the length of each part is \( \frac{L}{n} \) (where \( L \) is the original length).
- Therefore, the new spring constant \( k' \) for each part becomes:
\[ k' = n \cdot k \]

### Step 3: Determine the New Time Period
Now, we need to find the new time period \( T' \) for each part of the spring. Using the formula for the time period with the new spring constant:
\[ T' = 2\pi \sqrt{\frac{m}{k'}} \]
Substituting \( k' = n \cdot k \):
\[ T' = 2\pi \sqrt{\frac{m}{n \cdot k}} \]

### Step 4: Relate the New Time Period to the Original Time Period
We can express \( T' \) in terms of the original time period \( T \):
\[ T' = 2\pi \sqrt{\frac{m}{k}} \cdot \frac{1}{\sqrt{n}} = T \cdot \frac{1}{\sqrt{n}} \]

### Conclusion
Thus, the time period of each part of the spring after cutting it into \( n \) equal parts is:
\[ T' = \frac{T}{\sqrt{n}} \]