Two masses $A$ and $B$ having mass $m_a$ and $m_b$, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses $m_a$ and $m_b$ are $r_a$ and $r_b$, respectively. The angle between lines $OA$ and $OB$ is $90^{\circ}$.  If $m_a =10$ kg, $m_b=20$kg, $r_a=200$mm and $r_b=400$mm, then the balance mass to be placed at a radius of $200$ mm is ____ kg (round off to two decimal places).