Four masses $m_A=10(kg),m_B=8(kg),m_C=18(kg),$and $m_D=15(kg)$ are attached to a

shaft at radii of $R_A=20(mm),R_B=40(mm),R_C=30(mm),R_D=10(mm)$ and revolve in

the same plane. The angular position of the masses $A,B,C$ and $D$ are $0,60,135$ and

$270$ from $x$ axis, respectively. Find the magnitude of the balancing mass located at a

radius of $50(mm).$

$($Additional info: Use Balancing Rotary Masses, discussed in the

the magnitude of the balancing mass$).$

to find