When a load W is suspended from a wire, it elongates by 1.0 mm . If...

Let the original length of the wire be $L$, area of cross-section be $A$, and Young's modulus be $Y$.

When a load $W$ is suspended from the wire, the tension in the wire is $T = W$. The elongation is given by:

$\Delta L = \dfrac{WL}{AY} = 1.0 \text{ mm}$

When the same wire is passed over a pulley and a weight $W$ is attached to each of its two ends, the system is in equilibrium and the tension in the entire wire remains $T' = W$.

The total elongation of the wire is:

$\Delta L' = \dfrac{T'L}{AY} = \dfrac{WL}{AY} = 1.0 \text{ mm}$