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An annular ring of internal and outer radii \( r \) and \( R \) respectively oscillates in a vertical plane about a horizontal axis perpendicular to its plane and passing through a point on its outer edge. Calculate its time period and show that the length of an equivalent simple pendulum is \( \frac{3 R}{2} \) as \( r \rightarrow 0 \) and \( 2 R \) as \( r \rightarrow R \)
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