JEE Main 2026 — Electromagnetic Induction Question with Solution

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10\sin (\omega \mathrm{t})\mathrm{A}$, where $\omega =1000\mathrm{rad}./\mathrm{s}$. A circular conducting loop $(B)$ of radius 1 cm coaxially slided through the solenoid at a speed $v=1\mathrm{cm}/\mathrm{s}$. The r.m.s. current through the loop when the coil $B$ is inserted 10 cm inside the solenoid is $\alpha /\sqrt{2}\mu \mathrm{A}$. The value of $\alpha$ is $\_\_\_\_$.
[Resistance of the loop $=10\Omega$ ]