A uniformly conducting wire is bent to form a ring of mass ‘$m$’ and radius ‘$r$’ and the ring is placed on a rough horizontal surface with its plane horizontal. There exists a uniform and constant horizontal magnetic field of induction $B$. Now a charge $q$ is passed through the ring in a very small time interval $\Delta t$ and as a result the ring ultimately just becomes vertical. The value of g(acceleration due to gravity) is $\frac{{\pi }^2}{\lambda }{\left(\frac{qB}{m}\right)}^{2}r$ . Assume that friction is sufficient to prevent slipping and ignore any loss in energy. Find the value of $\lambda$ .