Physics Question from JEE Main 2023 · 6 April, Shift 2

A small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2}m\omega^2 r^2$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of the $n$th orbit will be proportional to: