A copper wire of length \(3\text{ m}\) is stretched by \(3\text{ mm}\) by applying an external force. The volume of the wire is \(600 \times 10^{-6}\text{ m}^3\). The elastic potential energy stored in the wire in stretched condition would be _______ J.
(Given Young modulus of copper \(= 1.1 \times 10^{11}\text{ N/m}^2\))

Given parameters:
\(L = 3\text{ m}\)
\(\Delta L = 3 \times 10^{-3}\text{ m}\)
\(V = 600 \times 10^{-6}\text{ m}^3\)
\(Y = 1.1 \times 10^{11}\text{ N/m}^2\)

Strain is given by:
\(\text{Strain} = \dfrac{\Delta L}{L} = \dfrac{3 \times 10^{-3}}{3} = 10^{-3}\)

Elastic potential energy stored in the wire is:
\(U = \dfrac{1}{2} \times \text{Stress} \times \text{Strain} \times \text{Volume}\)

Since \(\text{Stress} = Y \times \text{Strain}\):
\(U = \dfrac{1}{2} \times Y \times (\text{Strain})^2 \times V\)

Substituting the values:
\(U = \dfrac{1}{2} \times (1.1 \times 10^{11}) \times (10^{-3})^2 \times (600 \times 10^{-6})\)

\(U = \dfrac{1}{2} \times 1.1 \times 10^{11} \times 10^{-6} \times 600 \times 10^{-6}\)

\(U = \dfrac{1}{2} \times 1.1 \times 600 \times 10^{-1}\)

\(U = \dfrac{1}{2} \times 66 = 33\text{ J}\)

Answer: \(33\)