A wooden cylinder of diameter 4 r , height h and density $\rho / 3$ is kept on a hole of diameter $2 r$ of a tank, filled with water of density $\rho$ as shown in the figure. The height of the base of cylinder from the base of tank is H . Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, height of water level ( $\mathrm{h}_2$ in figure) for which the cylinder remains in original position without application of force is