A small particle of mass m moves in such a way that the potential energy $\;u=ar^2\;$ where a is a constant and r is the distance of particle from origin. Assuming Bohr's model of quantization of angular momentum and circular orbits. Then the radium of $\;n^{th}\;$ allowed orbit is

Question

$(a)\;r=(\large\frac{n^2 h^2}{82 a m \pi^{2}})^{\large\frac{1}{4}}\qquad(b)\;r=(\large\frac{n^2 h^2}{4 a m \pi^{2}})^{\large\frac{1}{4}}\qquad(c)\;r=(\large\frac{n^2 h^2}{8 a m \pi^{2}})^{\large\frac{1}{4}}\qquad(d)\;r=(\large\frac{n^2 h^2}{16 a m \pi^{2}})^{\large\frac{1}{4}}$