A particle of mass m is moving in a potential \(V(r)=-\frac{k}{r}\), where k is a positive constant. If \(\vec{L}\) and \(\vec{p}\) denote the angular momentum and linear momentum respectively, the value of α for which \(\vec{A}=\vec{L} \times \vec{p}+α m k \hat{r}\) is a constant of motion, is