Conditions for pulleys and strings

[voko]

I really don't see how you ended up with those conclusions. They are not conclusions, they are speculations at best, because you failed to back them up with a thorough FBD analysis.

Solve this: two masses a and b are hanging on a string though a pulley, which is a uniform thin ring of mass c and radius d. The string is massless and inextensible; static friction between the pulley and the string is very great. The pulley rotates about its axis without any friction.

 

[andyrk]

Why can't the tension remain same around the pulley even though it has mass? Ok the pulley needs to rotate so tensions are different, then how does a massless pulley rotate? The tensions are taken same even then it does rotate, then how is that?

 

[voko]

Why should the tensions be the same?

Regarding your question about the operation of massless pulleys: solve the problem above. Then see what happens with tensions as the pulley's mass goes to zero.