Problem

A small particle of mass

m

moves in such a way that the potential energy

U = \frac{1}{2} m^2 \omega^2 r^2

, where

\omega

is a constant and

r

is the distance of the particle from the origin. Assuming Bohr model of quantization of angular momentum and circular orbits, show that radius of the

n

th allowed orbit is proportional to

\sqrt{n}