The potential energy of a particle of mass m at a distance r from a fixed point O is given by V r = 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…

Question

The potential energy of a particle of mass m at a distance r from a fixed point O is given by V r = 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?

Aicharya · Accepted Answer

$\begin{aligned} & V=\frac{k r^2}{2} \ & L=m v R \ & =m \sqrt{\frac{k}{m}} R . R \ & =\sqrt{m k} R^2 \ & L=\sqrt{\frac{k}{m} R^2} \end{aligned}$

The potential energy of a particle of mass m at a distance r from a fixed point O is given by V r = k r 2 /…

Solution