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Question:

A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

g/2

5g/6

2g/3

g

Solution:

a = Rα (no slipping)
Also, τ = Iα and τ = TR
Using the relations, ⇒ T = Ia/R²
For hollow cylinder, I = mR²
⇒ T = ma
Now for block, ma = mg - T
ma = mg - ma
⇒ a = g/2