Tension in the Ring!

A ring of mass \(m\), radius \(R\), cross sectional area \(A\) and Young's modulus \(Y\) is kept on a smooth cone of radius \(2R\) and semi vertical angle \(45°\), as shown in the figure. Assume that the extension in the ring is small :-

\((A)\) The tension in the ring will be same throughout.

\((B)\) The tension in the ring will be independent of the radius of ring.

\((C)\) The extension in the ring will be \(\frac{mgR}{AY}\)

\((D)\) Elastic potential energy stored in the ring will be \(\frac{m^2g^2R}{8\pi YA}\)

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