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

1. A $v = \sqrt{\frac{k}{2m}}R$
2. B $v = \sqrt{\frac{k}{m}}R$
3. C $L = \sqrt{mk}R^{2}$
4. D $L = \sqrt{\frac{mk}{2}}R^{2}$

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Answers: B. $v = \sqrt{\frac{k}{m}}R$ · C. $L = \sqrt{mk}R^{2}$

System of Particles and Rotational Motion The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = \frac{k r^{2}}{2}$, where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O$, which of the following statements is (are) true? Watch this solved on the board The full walkthrough, written out a line at a time with narration explaining each step as it appears. Pause anywhere and ask why a line is there. Free to watch

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