Let's discuss a beautiful problem useful for Physics Olympiad based on Mass supported by a Hollow Cylinder.
The Problem:
A mass m is supported by a massless string wound on 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?
Solution:
For the mass m, the force equation stands as:
$$mg-T=ma....(i)$$
For the cylinder, the force equation is:
$$ T.R=mR^2(a/R)$$
Hence,
from above equation $$ T=ma $$
Now, putting the value of T in equation (i), we get
$$ma=2mg$$
$$\Rightarrow a=g/2$$
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