$A$ simple pendulum of length $L$ is suspended from the roof of a trolley. The trolley moves in a horizontal direction with an acceleration $a$. What would be the period of oscillation of the simple pendulum? [$g$ is the acceleration due to gravity]

• A
  $2 \pi \sqrt{L}(a^{2}+g^{2})^{-\frac{1}{4}}$
• B
  $2 \pi \sqrt{L}(a^{2}+g^{2})^{-\frac{1}{2}}$
• C
  $2 \pi \sqrt{\frac{L}{g+a}}$
• D
  $2 \pi \sqrt{\frac{L}{g-a}}$