A$,$ B$,$ C and D are four masses carried by a rotating shaft at radii $100$ mm$,150$ mm$,150$ mm and $200$ mm respectively. The planes in which the masses rotate are spaced at $500$ mm apart and the magnitude of the masses B$,$ C and D are $9$ kg$,5$ kg and $4$ kg respectively. Find the required mass A and the relative angular settings of the four masses so that the shaft shall be in complete balance.