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 `_|_` to plan 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 ratio of semicircular part)

Options

A. `Mr^(2) ((14+3pi )/( 3pi + 6))`
B. `Mr^(2)((pi+r)/( pi + 2r))`
C. `Mr^(2) ((3)/(4) pi ) `
D. `(1)/(2) Mr^(2)`

Answer

A