Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :

• A

  $\frac{1}{4}\frac{M{L}^2}{{\pi }^2}$
• B

  $\frac{2}{5}\frac{M{L}^2}{{\pi }^2}$
• Correct answer
  C

  $\frac{M{L}^2}{{\pi }^2}$
• D

  $\frac{1}{2}\frac{M{L}^2}{{\pi }^2}$

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