Force constant of a spring `(k)` is anonymous to

Options

A. `(YA)/(L)`
B. `(YL)/(A)`
C. `(AL)/(Y)`
D. `ALY`

Answer

To solve the problem regarding the force constant of a spring \( k \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Spring Force Equation**:
The force exerted by a spring is given by Hooke's Law:
\[ F = k \cdot \Delta L \]
where \( F \) is the force applied, \( k \) is the spring constant (force constant), and \( \Delta L \) is the change in length of the spring.

2. **Rearranging the Equation for Spring Constant**:
From the equation above, we can express the spring constant \( k \) as:
\[ k = \frac{F}{\Delta L} \]

3. **Introduce Young's Modulus**:
Young's modulus \( Y \) is defined as:
\[ Y = \frac{F \cdot L}{A \cdot \Delta L} \]
where \( L \) is the original length of the material, \( A \) is the cross-sectional area, and \( \Delta L \) is the change in length.

4. **Relate Spring Constant to Young's Modulus**:
We can rearrange the equation for Young's modulus to find \( \frac{F}{\Delta L} \):
\[ \frac{F}{\Delta L} = \frac{Y \cdot A}{L} \]

5. **Substituting into the Spring Constant Equation**:
Now, we can substitute this expression into the equation for \( k \):
\[ k = \frac{F}{\Delta L} = \frac{Y \cdot A}{L} \]

6. **Conclusion**:
Therefore, the spring constant \( k \) is related to Young's modulus \( Y \), the cross-sectional area \( A \), and the original length \( L \) of the spring as:
\[ k = \frac{Y \cdot A}{L} \]

### Final Answer:
The force constant of a spring \( k \) is given by:
\[ k = \frac{Y \cdot A}{L} \]