A cord of mass m length L, area of cross section A and Young's modulus y is hanging from a ceiling with the help of a rigid support. The elogation developed in the wire due to its own weight is

Options

A. `(mgl)/(YA)`
B. `(mgl)/(2YA)`
C. `(2mgl)/(YA)`
D. `(2mgl)/(3YA)`

Explanation

To find the elongation developed in a cord of mass \( m \), length \( L \), area of cross-section \( A \), and Young's modulus \( Y \) due to its own weight, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Effective Length**:
The weight of the cord acts at its center of mass, which is located at the midpoint of the cord. Therefore, the effective length \( L_{\text{eff}} \) for the elongation calculation is:
\[
L_{\text{eff}} = \frac{L}{2}
...