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 `

Options

A. `(d^(2) g^(2) Al^(3))/(6Y)`
B. `(dg A l^(3))/(6Y)`
C. `(d^(2) g^(2) Al^(3))/(3Y)`
D. `(d^(2) g^(2) A^(2) l^(3))/(3Y)`

Answer

A

Explanation

`int dU = int_(0)^(L) (1)/(2) (d^(2) g^(2) A)/(Y)x^(2) dx`
`( :. int (1)/(2) [("Stress")/(Y)]^(2)xx Vol)`