The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = kr^2 / 2$,where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. 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?
$(A)$ $v = \sqrt{\frac{k}{2m}} R$
$(B)$ $v = \sqrt{\frac{k}{m}} R$
$(C)$ $L = \sqrt{mk} R^2$
$(D)$ $L = \sqrt{\frac{mk}{2}} R^2$

• A
  $A, C$
• B
  $B, C$
• C
  $A, D$
• D
  $A, C, D$