Let angular velocity of system is w .For ball c , v_0=3wL w=\\dfrac{v_0}{3L} For ball A , force due to rotation, F_A=mw^2L=\\dfrac{mv_0}{9L} Similarly, F_B=\\dfrac{2mv_0}{9L} F_C=\\dfrac{mv_0}{3L} So, tension in the string joining B and C is \\dfrac{mv_0}{3L} T_1=\\dfrac{mv_0}{3L} T_2=\\dfrac{2mv_0}{9L}+\\dfrac{mv_0}{3L}=\\dfrac{5mv_0}{9L} So, T_1:T_2:T_3 will be \\dfrac1{3}:\\dfrac5{9}:\\dfrac2{3} \\implies 3:5:6