A particle of mass m and charge -Q is constrained to move along the axis of a ring of radius R .The ring carries a uniform charge density $\;+ \lambda\;$ along its length . Initially the particle is in the centre of the ring . Now it is displaced slightly along the axis of ring it's time period of oscillation is

Question

$(a)\;2 \pi\;\sqrt{\large\frac{\in_{0}\;m\;R^2}{\lambda\;Q}}\qquad(b)\;\pi\;\sqrt{\large\frac{2 \in_{0}\;m\;R^2}{\lambda\;Q}}\qquad(c)\;2 \pi\;\sqrt{\large\frac{2 \in_{0}\;m\;R^2}{\lambda\;Q}}\qquad(d)\; 4\pi\;\sqrt{\large\frac{2 \in_{0}\;m\;R^2}{\lambda\;Q}}$