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A thin ring has a radius \( R \), density \( \rho \) and Youngs modulus \( Y \). The ring is rotated in its
\( \mathrm{P} \) own plane about an axis passing through its

W centre with angular velocity \( \omega \). Then the small increase in its radius is :-
(1) \( d R=\frac{\rho \omega^{2} R^{3}}{Y} \)
(2) \( \mathrm{dR}=\frac{3 \rho \omega^{2} \mathrm{R}^{3}}{\mathrm{Y}} \)
(3) \( \mathrm{dR}=\frac{6 \rho \omega^{2} \mathrm{R}^{3}}{\mathrm{Y}} \)
(4) \( d R=\frac{\rho \omega^{2} R^{3}}{2 Y} \)
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