1. Use the relation for elongation of a wire

For a wire of length $L$, area $A$, and Young's modulus $Y$, the elongation under tension $T$ is

So, elongation is directly proportional to the tension in the wire.

2. Given case

When a load $W$ is hung from the wire, the tension in the wire is

Hence the elongation is given as

So,

3. Wire over a pulley with weights $W$ and $W$ at the two ends

If the pulley is ideal and the two equal weights $W$ are hanging at the two ends, the system is in equilibrium.

For a light wire over a smooth pulley, the tension throughout the wire is still

4. Find the elongation

Since elongation depends on tension, and the tension is again $W$, the total elongation of the wire remains

So the elongation is

5. Check options

• A: $l$ ✅
• B: $2l$ ❌
• C: zero ❌
• D: $l/2$ ❌

Therefore, the correct option is A.