When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.

A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:
1. $\frac{YxA}{2L}$

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

A \(5\) m long wire is fixed to the ceiling. A weight of \(10\) kg is hung at the lower end and is \(1\) m above the floor. The wire was elongated by \(1\) mm. The energy stored in the wire due to stretching is:
1. zero                                 
2. \(0.05\) J
3. \(100\) J                          
4. \(500\) J