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?


For the mass m, the force equation stands as:


For the cylinder, the force equation is:

$$ T.R=mR^2(a/R)$$


from above equation $$ T=ma $$

Now, putting the value of T in equation (i), we get


$$\Rightarrow a=g/2$$