A thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^{\circ}$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

• A

  $\frac{\sqrt{2} M L^2}{24}$
• B

  $\frac{M L^2}{24}$
• Correct answer
  C

  $\frac{M L^2}{12}$
• D

  $\frac{M L^2}{6}$

Hence, the correct answer is option: 'C'.