In the multi$-$rotor system shown above, $m_1=4kg,m_2=4kg,r_1=50mm,r_2=74mm,z_1=95mm,z_2=430mm,{}_1=127,2=249.$ We have $2kg$ masses to balance the multi$-$rotor shaft. Answer questions $a,b,$ c and d accordingly.

a$-)$ Determine the radius $(mm)$ where a $2kg$ mass will be placed on the $R$ plane.

b$-)$ Determine the angle $($degrees$)$ at which the $2kg$ mass will be placed on the $R$ plane.

c$-)$ Determine the radius $(mm)$ where a $2kg$ mass will be placed on the $L$ plane.

d$-)$ Determine the angle $($degrees$)$ at which the $2kg$ mass will be placed on the $L$ plane.