The potential energy of a particle of mass m at a distance r from a fixed point O is given by $V\left(r\right)=k{r}^2/2$, 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?

• A

  $v=\sqrt{\frac{k}{2m}}R$
• Correct answer
  B

  $v=\sqrt{\frac{k}{m}}R$
• Correct answer
  C

  $L=\sqrt{mk}{R}^2$
• D

  $L=\sqrt{\frac{mk}{2}}{R}^2$

Solution

$V=\frac{k{r}^2}{2}$
$L=mvR$
$=m\sqrt{\frac{k}{m}} R.R$
$=\sqrt{mk} R^2$
$L=\sqrt[m]{\frac{k}{m}{R}^2}$

Hence, the correct answer is options: 'B', 'C'.