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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 :

$\begin {array} {1 1} (1)\;\large\frac{\sqrt 2 \: ML^2}{24} & \quad (2)\;\large\frac{ML^2}{24} \\ (3)\;\large\frac{ML^2}{12} & \quad (4)\;\large\frac{ML^2}{6} \end {array}$

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