A particle of mass $$m$$, and angular momentum $$\ell$$ is moving in a circular orbit of radius $$r_0$$ under the influence of an attractive force $$\vec{F}(r)=-\dfrac{k}{r^2}\hat{r}$$. Keeping its angular momentum unchanged, the particle is displaced radially by a small distance $$\delta r\ll r_0$$, due to which its radial distance varies periodically. The corresponding time period is:

A

$$\dfrac{2\pi\ell^3}{mk^2}$$

B

$$2\pi\sqrt{\dfrac{m}{k}}$$

C

$$\dfrac{2\pi\ell^3}{3mk^2}$$

D

$$\dfrac{2\pi\ell^3}{5mk^2}$$