A wire of length l and cross-sectional are A is suspended at one of its ends from a ceiling. What will be its strain energy due to its own weight, if the density and Young's modulus of the material of the wire be d and Y?

Explanation

To find the strain energy stored in a wire of length \( L \) and cross-sectional area \( A \) due to its own weight, we can follow these steps:

### Step 1: Understand the Forces Acting on the Wire
The wire is suspended from one end, and its own weight creates a varying force along its length. The weight of a small segment \( dx \) of the wire at a distance \( x \) from the lower end can be expressed as:
\[ dF = \text{mass} \times g = (\rho \cdot A \cdot dx) \cdot g = \rho \cdot A \cdot g \cdot dx \]
where \( \rho \) is the density of the material, \( A \) is the cross-sectional area, and \( g \) is the acceleration due to gravity.
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