A hollow cylinder of mass M has outer radius R₂ and inner radius R_1. Its M.I about an axis parallel to its axis and tangential to the outer surface is

Dear Gautham.

The total energy in the system is given by


T = 1/2 m2 Vo^2 + 1/2 m1 Vo^2 + 1/2 I wo^2 
= 1/2 m2 Vf^2 + 1/2 m1 Vf^2 + 1/2 I wf^2 - m1gd + uk m2g d

where Vo,Vf are the initial and final velocity of the blocks, wo/wf are the initial and finalangular velocity of the pulley, I is the moment of inertia of the pulley. w is related to V as

Vo = R2 wo and Vf = R2 wf. 

Also, the moment of inertia is given by

I = 1/2 m (R2^2 + R1^2)

You have all the data now, you can go ahead and solve for Vf in the energy equation above. After that, you can calculate wf.

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert

Approved