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Q.  A wire frame AOPQB, lying in the horizontal plane, is free to rotate about a vertical axis passing through center C of the same circle and perpendicular to plane of AOPQB. The mass M of the frame is uniformly distributed over its whole length. The moment of inertia of the frame about this axis, is
(OA = QB = r and CP = r the radius of semicircular part) :-

$$\begin{gathered} \left(A\right) M{r}^2 \left(\frac{14 + 3\mathrm{\pi }}{3\mathrm{\pi } + 6}\right) \left(B\right) M{r}^2 \left(\frac{14 + 3\mathrm{\pi }}{\mathrm{\pi } + 2}\right) \\ \left(C\right) \frac{M{r}^2}{2} \left(\frac{\mathrm{\pi }}{2 + \mathrm{\pi }}\right) \left(D\right) \frac{1}{2}M{r}^2 \end{gathered}$$