The time period of a freely suspended magnet is 4 seconds. If it is broken in length into two equal parts and one part is suspended in the same way, then its time period will be

Options

A. `4 sec`
B. `2 sec`
C. `0.5 sec`
D. `0.25 sec`

Explanation

To solve the problem, we need to understand how the time period of a freely suspended magnet changes when it is cut into equal parts. The time period of a magnet is related to its length, and when the length is halved, the time period is affected accordingly.

### Step-by-Step Solution:

1. **Identify the Original Time Period**:
The original time period \( T \) of the freely suspended magnet is given as 4 seconds.

2. **Determine the Length of the Original Magnet**:
Let's denote the original length of the magnet as \( L \). For the sake of calculation, we can assume that the original magnet is of length \( 2L \) (this is just for understanding, as the exact length isn't necessary for the calculation).

3. **Cut the Magnet into Two Equal Parts**:
When the magnet is cut into two equal parts, each part will have a length of \( L \).

4. **Understand the Relationship Between Length and Time Period**:
The time period \( T \) of a magnet is inversely proportional to the square root of its length. This means that if the length is halved, the time period will change according to the formula:
\[ T' = T \cdot \sqrt{\frac{L}{L'}} \]
where \( L' \) is the new length after cutting.

5. **Calculate the New Time Period**:
Since the original length was \( 2L \) and the new length after cutting is \( L \), we can substitute:
\[ T' = T \cdot \sqrt{\frac{2L}{L}} = T \cdot \sqrt{2} \]
However, since we are cutting the magnet into two equal parts, we can also use the formula:
\[ T' = \frac{T}{N} \]
where \( N \) is the number of equal parts the magnet is cut into. Here, \( N = 2 \).

6. **Substituting the Values**:
\[ T' = \frac{4 \text{ seconds}}{2} = 2 \text{ seconds} \]

7. **Conclusion**:
The time period of the new magnet after cutting it into two equal parts is 2 seconds.

### Final Answer:
The time period of the magnet when one part is suspended is **2 seconds**.

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