Magnetic Flux & Faraday's Law question from JEE Main 2026 (2 Apr, Shift 1)

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $N,\ A$ and $r$ respectively. For a second coil number of turns, area of the coil and radius of the coil wire are $2N,\ 2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt{2}\,\alpha P$. The value of $\alpha$ is ______.