If a spring of force constant k is divided into n equal parts , then force constant of each part is

Options

A. k
B. `(k)/(n)`
C. no force will act
D. nk

Explanation

To solve the problem, we need to understand the relationship between the spring constant (k), the length of the spring (l), and how dividing the spring affects the spring constant of each part.

### Step-by-Step Solution:

1. **Understand the Spring Constant**:
The spring constant (k) is a measure of the stiffness of a spring. It is defined by Hooke's Law, which states that the force (F) exerted by a spring is proportional to the displacement (x) from its equilibrium position:
\[ F = kx \]

2. **Relationship Between Spring Constant and Length**:
The spring constant is inversely proportional to the length of the spring. This means:
\[ k \propto \frac{1}{l} \]
or
\[ k = \frac{C}{l} \]
where C is a constant.

3. **Dividing the Spring**:
If we have a spring of length \( l \) with a spring constant \( k \), and we divide this spring into \( n \) equal parts, the length of each part will be:
\[ l' = \frac{l}{n} \]

4. **Finding the New Spring Constant**:
Since the spring constant is inversely proportional to the length, we can express the new spring constant \( k' \) for each part as:
\[ k' = \frac{C}{l'} = \frac{C}{\frac{l}{n}} = \frac{C \cdot n}{l} \]
From the original spring constant \( k = \frac{C}{l} \), we can substitute \( C \):
\[ k' = n \cdot k \]

5. **Conclusion**:
Therefore, the spring constant of each part when the original spring is divided into \( n \) equal parts is:
\[ k' = n \cdot k \]

### Final Answer:
The force constant of each part is \( n \cdot k \).

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