A very thin bar of length \(\ell\) and negligible inertia connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) that have inertias \(4 m\) and \(m\), respectively (Figure P12.11). When this rod-block system is made to spin with no translational motion and no mechanical pivor, each block moves through a circular path in space, with circumferences \(C_{A}\) and \(\mathrm{C}_{\mathrm{B}}\). Determine the ratio \(\mathrm{C}_{\mathrm{A}} / \mathrm{C}_{\mathrm{B}}\).

Data from Figure P12.11

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A B