A particle of mass m is moving in a stable circular orbit of radius with angular momentum L. For a potential energy V(r) = βrk (β > 0 and k > 0), which of the following options is correct?
1
\(k=3, r_0=\left(\frac{3 L^2}{5 m \beta}\right)^{1 / 5} \)
2
\(k=2, r_0=\left(\frac{L^2}{2 m \beta}\right)^{1 / 4} \)
3
\(k=2, r_0=\left(\frac{L^2}{4 m \beta}\right)^{1 / 4} \)
4
\(k=3, r_0=\left(\frac{5 L^2}{3 m \beta}\right)^{1 / 5} \)