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A particle of mass \( m \) moves in a circular orbit of radius \( r \). It is under the influence of a force field where its potential energy is given as \( U=a r^{2} \) where \( a \) is a positive constant. Assume that Bohrs model of quantization of angular momentum is applicable and calculate the radius of \( n^{\text {th }} \) allowed orbit.
(a) \( \left[\frac{n^{2} h^{2}}{6 a m \pi^{2}}\right]^{1 / 4} \)
(b) \( \left[\frac{n^{2} h^{2}}{8 a m \pi^{2}}\right]^{1 / 4} \)
(c) \( \left[\frac{n^{2} h^{2}}{4 a m \pi^{2}}\right]^{1 / 4} \)
(d) \( \left[\frac{n^{2} h^{2}}{2 a m \pi^{2}}\right]^{1 / 4} \)
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