$A$ uniform rod $AB$ of mass $m$ and length $l$ is hinged at its midpoint $C$. The left half $(AC)$ of the rod has linear charge density $-\lambda$ and the right half $(CB)$ has $+\lambda$,where $\lambda$ is constant. $A$ large non-conducting sheet of uniform surface charge density $\sigma$ is also present near the rod. Initially,the rod is kept perpendicular to the sheet. The end $A$ of the rod is initially at a distance $d$. Now,the rod is rotated by a small angle $\theta$ in the plane of the paper and released. The time period of small angular oscillations is:

• A
  $T = 2\pi \sqrt{\frac{m\epsilon_0}{3\lambda\sigma}}$
• B
  $T = 2\pi \sqrt{\frac{2m\epsilon_0}{\lambda\sigma}}$
• C
  $T = 2\pi \sqrt{\frac{4m\epsilon_0}{3\lambda\sigma}}$
• D
  $T = 2\pi \sqrt{\frac{2m\epsilon_0}{3\lambda\sigma}}$