A problem by crazy singh

Level pending

two circular loops \( A \) and \( B \) of radii \( R \) and \( 2R \) respectively are made of the same wire. The ratio of their moment of inertia about the axis passing through the center and perpendicular to their planes is given by \( \frac{a}{b} \). where \( a \) and \( b \) are co-prime integers. then \( a + b \) is equal to?

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