b
since rod is bent at the middle, so each part of it will have the same length \(\left(\frac{L}{2}\right)\) and \(\operatorname{mass}\left(\frac{M}{2}\right)\) as shown

Moment of inertia of each part through its one end

\(=\frac{1}{3}\left(\frac{M}{2}\right)\left(\frac{L}{2}\right)^{2}\)

Hence, net moment of inertia of complete structure through its middle point \(O\) is.

\(I=\frac{1}{3}\left(\frac{M}{2}\right)\left(\frac{L}{2}\right)^{2}+\frac{1}{3}\left(\frac{M}{2}\right)\left(\frac{L}{2}\right)^{2}\)

\(=\frac{1}{3}\left[\frac{M L^{2}}{8}+\frac{M L^{2}}{8}\right]=\frac{M L^{2}}{12}\)