A sphere of mass \(m\), radius \( r \) moves in a circle with constant speed \(v\), always touching the inner surface of a fixed hollow cylinder with radius \( R \). The top view of the system is shown. All surfaces are smooth. If the magnitude of the normal reaction (in Newtons) exerted by the cylinder on the sphere is \(\frac{ A } { B } \) where \( A \) and \( B \) are co-prime positive integers, what is \( A + B \)?

- \( m = 0.1 \text{ kg} \)
- \( v = 1 \text{ m s}^{-1} \)
- \( r = 0.1 \text{ m} \)
- \( R = 1 \text{ m} \)

This problem is part of the set - Circular Motion Practice

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