A wire having a length `L` and cross- sectional area `A` is suspended at one of its ends from a ceiling . Density and young's modulus of material of the wire are `rho` and `Y`, respectively. Its strain energy due to its own weight is `(rho^(2)g^(2)AL^(3))/(alphaY)`. Find the value of `alpha `

Explanation

To find the value of \( \alpha \) in the expression for the strain energy of a wire due to its own weight, we can follow these steps:

### Step 1: Understand the Problem
We have a wire of length \( L \) and cross-sectional area \( A \) suspended from one end. The density of the wire is \( \rho \) and its Young's modulus is \( Y \). We need to find the value of \( \alpha \) in the expression for the strain energy due to the wire's own weight, given as:

\[ \text{Strain Energy} = \frac{\rho^2 g^2 A L^3}{\alpha Y} \]
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