Magnetic Flux & Faraday's Law question from JEE Main 2026 (5 Apr, Shift 2)

A circular loop of radius 20 cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = \left(2t^{2}+2t+3\right)T$. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3\text{ s}$ is $\frac{\alpha}{50}\text{ A}$. The value of $\alpha$ is ______. (Take $\pi = 22/7$)