Step 1: Drawing free body diagrams [Ref. Fig 1 & 2]
Angular velocity (ω) will be same for all
Step 2: Writing force equation for A, B and C
Solving in ground frame:
Applying Newton's Second Law on A, B, and C along the centripetal direction
(Considering direction towards center as positive)
∑F=mac
Where, ac= Centripetal acceleration =ω2r, r= radius
For C–––––––
T1=maC=mω23l ....(1)
For B–––––––
T2−T1=maB
⇒ T2=mω23l+mω22l=mω25l ....(2)
For A–––––––
T3−T2=maA
⇒T3=mω25l+mω2l=mω26l ....(3)
Step 3: Ratio calculation
From eqn. (1), (2) and (3)
T1:T2:T3=3:5:6
Hence option D is correct