The four masses $A,B,C$ and $D$ are $100kg,150kg,120kg$ and $130$ kg attached to a shaft and revolve in the same plane. The corresponding rad of rotation are $22\mathrm{.}5cm,17\mathrm{.}5cm,25cm$ and $30$ cm and the angles measured from A are $45,120,$ and $255.$ Find the position and magnitude of the balancing mass, if the radius of rotation is $60$ cm $.$