1. Use the formula for resistivity

   The specific resistance (resistivity) of a wire is $S_1 = X\left(\frac{\pi r^2}{L}\right),$ where:

   • $X$ = resistance of the wire,
   • $L$ = length of the wire,
   • $r$ = radius of the wire.

2. Recall the basic relation

   Resistance of a wire is given by $X = \rho \frac{L}{A},$ where $\rho$ is the resistivity and $A = \pi r^2$.

   Therefore, $\rho = X\frac{A}{L} = X\left(\frac{\pi r^2}{L}\right).$

   So $S_1$ is just the resistivity of the material.

3. What happens if the length is doubled?

   If the wire is stretched in length from $L$ to $2L$ but the material remains the same, then specific resistance (resistivity) does not depend on dimensions of the wire.

   Resistivity depends only on the nature of material and temperature.

4. Hence

   Even if the length becomes doubled, the specific resistance remains unchanged: $S_1' = S_1.$

5. Check options

   • A: $\dfrac{S_1}{4}$ ❌
   • B: $2S_1$ ❌
   • C: $\dfrac{S_1}{2}$ ❌
   • D: $S_1$ ✅

Therefore, the correct answer is Option D.