A small particle of mass m moves in such a way that its potential energy U=1/2 m ω^2 r^2 where ω is constant and r is the distance of the particle…

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