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The potential energy of a particle of mass \( \mathrm{m} \) at a distance \( \mathrm{r} \) from a fixed point \( \mathrm{O} \) is given by \( \mathrm{V}(\mathrm{r})=\mathrm{kr}^{2} / \) 2 , where \( k \) is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius \( R \) about the point \( \mathrm{O} \). If \( v \) is the speed of the particle and \( L \) is the magnitude of its angular momentum
\( \mathrm{P} \) about \( \mathrm{O} \), which of the following statements is (are) true?

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(A) \( v=\sqrt{\frac{k}{2 m}} R \)
(B) \( v=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}} \mathrm{R} \)
(C) \( \mathrm{L}=\sqrt{\mathrm{mk}} \mathrm{R}^{2} \)
(D) \( \mathrm{L}=\sqrt{\frac{\mathrm{mk}}{2}} \mathrm{R}^{2} \)
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