a b c d

c

$\text{Let x is the length of the wire, then length of solenoid is}$ $ x = 2\pi rN$ $ N = \frac{x}{2\pi r}$ $\text{Area of cross section} A = \pi r^2$ $\text{Self Inductance} L = \frac{\mu_0 N^2A}{l}$ $\Rightarrow L = \frac{\mu_0 \pi r^2 \frac{x^2}{(2\pi r)^2}}{l}$ $\Rightarrow x = \sqrt{\frac{4\pi Ll}{\mu_0}}$